If you had $500 to put into a savings account with 8% interest , how would you know which bank to choose, if you plan to withdraw everything after 10 years—one that pays simple interest or compound interest? Explain.

Answer:

[tex]A(t) = 48833e^{0.0389t}[/tex]

The exponential growth rate is r = 0.0389

Step-by-step explanation:

An exponential function for the number of women graduating from​ 4-yr colleges in t years after 1930 can be given by the following equation:

[tex]A(t) = A(0)e^{rt}[/tex]

In which A(0) is the initial amount, and r is the exponential growth rate, as a decimal.

1930​, when 48,833 women earned a​ bachelor's degree

This means that [tex]A(0) = 48833[/tex]

2004​, when approximately 870,000

2004 is 74 years after 1930, which means that [tex]A(74) = 870000[/tex]

Applying to the equation:

[tex]A(t) = A(0)e^{rt}[/tex]

[tex]870000 = 48833e^{74r}[/tex]

[tex]e^{74r} = \frac{870000}{48833}[/tex]

[tex]\ln{e^{74r}} = \ln{\frac{870000}{48833}}[/tex]

[tex]74r = \ln{\frac{870000}{48833}}[/tex]

[tex]r = \frac{\ln{\frac{870000}{48833}}}{74}[/tex]

[tex]r = 0.0389[/tex]

So

[tex]A(t) = A(0)e^{rt}[/tex]

[tex]A(t) = 48833e^{0.0389t}[/tex]

To find an exponential function that fits the given data, determine the values of the base and the exponent. The exponential function that fits the data is y = 2.311 * 1.049^x. The exponential growth rate is approximately 1.049.

To find an exponential function that fits the data, we need to determine the values of the base and the exponent. Let's let the year be the input, x, and the number of women graduating be the output, y. The general form of an exponential function is y = ab^x, where a is the initial value and b is the growth rate. Substituting the given data, we have the equation:

48,833 = a * b1930

870,000 = a * b2004

By dividing the second equation by the first equation, we can eliminate a:

870,000 / 48,833 = (a * b2004) / (a * b1930)

17.821 = b2004-1930

17.821 = b74

Taking the log base b of both sides, we get:

logb 17.821 = 74

Solving for b using logarithmic properties, we find:

b = 17.8211/74

b ≈ 1.049

Now that we have the value of b, we can substitute it into one of the original equations to find a:

48,833 = a * 1.0491930

Solving for a, we get:

a ≈ 2.311

Therefore, the exponential function that fits the data is y = 2.311 * 1.049x. The exponential growth rate is approximately 1.049.

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Answer:

Correlation coefficient 'r' would be lower.

Step-by-step explanation:

Correlation is co movement relationship between two variables.

Correlation coefficient 'r' is positive, when variables move in same direction. 'r' is negative when variables move in opposite direction. So, 'r' lies between -1 (perfect negative correlation) & +1 (perfect positive correlation). High 'r' magnitude reflects strong correlation between the variables, Low 'r' reflects  weak weak correlation between the variables.

Correlation studied between amount of daily exercise and weight  : It is negative as exercise & weight are negatively correlated - more exercise, less weight & less exercise, more weight. 'r' is given = -0.21

If sample is restricted to people weighing less than 180 pounds : It would lead to fall in 'r'. Such because these low weight people are likely to have good natural metabolic rate, naturally slim body physique / figure. So, in their case, exercise & body weight are likely to be less (weakly) correlated than normal case.

Find the given attachments for complete answer

Answer:

The 95% confidence interval for the proportion for the American adults who believed in astrology is (0.23, 0.27).

This means that we can claim with 95% confidence that the true proportion of all American adults who believed in astrology is within 0.23 and 0.27.

Step-by-step explanation:

We have to construct a 95% confidence interval for the proportion.

The sample proportion is p=0.25.

[tex]p=X/n=501/2004=0.25[/tex]

The standard deviation can be calculated as:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.25*0.75}{2004}}=\sqrt{ 0.000094 }=0.01[/tex]

For a 95% confidence interval, the critical value of z is z=1.96.

The margin of error can be calculated as:

[tex]E=z\cdot \sigma_p=1.96*0.01=0.0196[/tex]

Then, the lower and upper bounds of the confidence interval can be calculated as:

[tex]LL=p-E=0.25-0.0196=0.2304\approx0.23\\\\UL=p+E=0.25+0.0196=0.2696\approx 0.27[/tex]

The 95% confidence interval for the proportion for the American adults who believed in astrology is (0.23, 0.27).

This means that we can claim with 95% confidence that the true proportion of all American adults who believed in astrology is within 0.23 and 0.27.

Answer:

a parallelogram, trapezium and rhombus

Step-by-step explanation:

The expected number of tests using the group testing procedure is 1.75.

To find the expected number of tests using the group testing procedure, we need to consider the different possible outcomes. Let's break it down:

If no one has the disease (probability = 1 - p), then only one test is required.

If at least one individual has the disease (probability = p), the test on the combined sample will yield a positive result, and then the n individual tests will be carried out.

Therefore, the expected number of tests is:

Expected number of tests = (probability of no disease) * (number of tests in this case) + (probability of disease) * (number of tests in this case)

For the first case, the number of tests is 1.

For the second case, the number of tests is n + 1, because one additional test is required after the positive result from the combined sample.

Substituting the values, Expected number of tests = (1 - p) * 1 + p * (n + 1)

Given p = 0.15 and n = 5, substituting the values we get:

Expected number of tests = (1 - 0.15) * 1 + 0.15 * (5 + 1) = 0.85 * 1 + 0.15 * 6 = 0.85 + 0.9 = 1.75

Therefore, the expected number of tests using this procedure is 1.75.

Answer:

100

Step-by-step explanation:

43+57=100

I added 3+7=10

Then 40+50=90 and added them

90+10=100

Answer: 100

Step-by-step explanation:

You know that 3+7=10

You know that 40+50=90

90+10=100

Answer:

Step-by-step explanation:

Z=-1.5

-1.5=2.5

Final answer:

To find the area under the standard normal curve between z = -1.5 and z = 2.5, subtract the area to the left of z = -1.5 from the area to the left of z = 2.5 to be 0.927.

Explanation:

To find the area under the standard normal curve between z = -1.5 and z = 2.5, we can subtract the area to the left of z = -1.5 from the area to the left of z = 2.5.

Using the z-table, we can find that the area to the left of z = -1.5 is approximately 0.0668 and the area to the left of z = 2.5 is approximately 0.9938.

Therefore, the area between z = -1.5 and z = 2.5 is approximately 0.9938 - 0.0668 = 0.927.

Answer:

Option E) The population percentage of Japanese who believes in the complete recovery of Japan is Between 64.82% and 69.18%.

Step-by-step explanation:

Gallup asked 2100 Japanese, so the sample size is:

n = 2100

67% of the Japanese answered in affirmative. This means the proportion of population which answered in favor or affirmative is:

p = 67%

Based on his findings, Gallup constructed a confidence interval. We have to identify the correct confidence interval i.e. the population percentage of Japanese who believes in the complete recovery of Japan.

The confidence interval will always be in form of a range of values i.e. between two values: A lower limit and an upper limit. This automatically removes choices A and B from the list of correct answers.

Furthermore, the confidence interval is symmetric about the sample proportion(p), as the formula to calculate the confidence interval for a population proportion is:

( p - M.E, p + M.E )

where M.E means Margin of Error. Since, same value(M.E) is added to and subtracted from the sample proportion(p), the confidence interval will be symmetric about the sample proportion.

So, now we will find if the values in choices C,D and E are symmetric about the mean or not. If the values are symmetric the difference of the values in each option from p = 67% must be same.

Choice C)

60% and 70%

We can easily tell that these values are not symmetric about 67%. Therefore, this cannot be the answer.

Choice D)

65.13% and 70.21%

67% - 65.13% = 1.87%

70.21% - 67% = 3.21%

These two values are not symmetric either. So these cannot be our confidence interval.

Choice E)

64.82% and 69.18%

67% - 64.82% = 2.18%

69.18% - 67% = 2.18%

These two values are same distance apart from 67%, this means they are symmetric about the sample proportion. Hence, choice E is the correct confidence interval. The Margin of Error is 2.18%

The population percentage of Japanese who believes in the complete recovery of Japan is Between 64.82% and 69.18%.

Answer:

clearing picture

Step-by-step explanation:

Answer:

The platform cannot hold both elephants.

Step-by-step explanation:

This problem is solved by conversion of units.

Elephant A weighs 11,028 pounds

Elephant B weighs 5 1/2 = 5.5 tons

The platform can hold 22,000 pounds

To see if the platform holds both elephants, the first step is converting the weigth of Elephant B to pounds.

Each ton has 2000 pounds.

So 5.5 tons have 5.5*2000 = 11000 pounds.

So Elephant B weighs 11000 pounds

Combined weights of Elephants A and B

11,028 + 11,000 = 22,028 > 22,000

The platform cannot hold both elephants.

Answer:

The fifth degree Taylor polynomial of g(x) is increasing around x=-1

Step-by-step explanation:

Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:

[tex]P_5(x)=g(-1)+g'(-1)\,(x+1)+g"(-1)\, \frac{(x+1)^2}{2!} +g^{(3)}(-1)\, \frac{(x+1)^3}{3!} + g^{(4)}(-1)\, \frac{(x+1)^4}{4!} +g^{(5)}(-1)\, \frac{(x+1)^5}{5!}[/tex]

and when you do its derivative:

1) the constant term renders zero,

2) the following term (term of order 1, the linear term) renders: [tex]g'(-1)\,(1)[/tex] since the derivative of (x+1) is one,

3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero

Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is: [tex]g'(-1)= 7[/tex] as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1

Answer:

(a) The test statistic value is, 5.382.

(b) Retain the null hypothesis.

Step-by-step explanation:

A Chi-square test for goodness of fit will be used in this case.

The hypothesis can be defined as:

H₀: The observed frequencies are same as the expected frequencies.

Hₐ: The observed frequencies are not same as the expected frequencies.

The test statistic is given as follows:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]

The information provided is:

Observed values:

Half Pint: 36

XXX: 35

Dark Night: 9

TOTAL: 80

The expected proportions are:

Half Pint: 40%

XXX: 40%

Dark Night: 20%

Compute the expected values as follows:

E (Half Pint) [tex]=\frac{40}{100}\times 80=32[/tex]

E (XXX) [tex]=\frac{40}{100}\times 80=32[/tex]

E (Dark night) [tex]=\frac{20}{100}\times 80=16[/tex]

Compute the test statistic as follows:

[tex]\chi^{2}=\sum\limits^{n}_{i=1}{\frac{(O_{i}-E_{i})^{2}}{E_{i}}}[/tex]

    [tex]=[\frac{(36-32)^{2}}{32}]+[\frac{(35-32)^{2}}{32}]+[\frac{(9-16)^{2}}{16}][/tex]

    [tex]=3.844[/tex]

The test statistic value is, 5.382.

The degrees of freedom of the test is:

n - 1 = 3 - 1 = 2

The significance level is, α = 0.05.

Compute the p-value of the test as follows:

p-value = 0.1463

*Use a Ch-square table.

p-value = 0.1463 > α = 0.05.

So, the null hypothesis will not be rejected at 5% significance level.

Thus, concluding that the production of the premium lagers matches these consumer preferences.

Answer:

d = 2

Step-by-step explanation:

We have four unknown numbers a, b, c, d

It is given that the mode is 3,

Since the mode is 3 then at least two numbers are 3.

It is given that the median is 3,

Since the median is 3 which means the middle two values must be 3

a, 3, 3, d

It is given that the mean of the four numbers is 4,

Since the mean of the four number is 4 then

mean = (a + 3 + 3 + d)/4

4 = (a + 6 + d)/4

4*4 = a + 6 + d

16 = a + 6 + d    eq. 1

It is given that the range is 6,

Since the range is 6 which is the difference between highest and lowest number that is

a - d = 6

a = 6 + d    eq. 2

Substitute the eq. 2 into eq. 1

16 = a + 6 + d

16 = (6 + d) + 6 + d

16 = 12 + 2d

2d = 16 - 12

d = 4/2

d = 2

Substitute the value of d into eq. 2

a = 6 + d

a = 6 + 2

a = 8

so

a, b, c, d = 8, 3, 3, 2

Verification:

a ≤ b ≤ c ≤ d

8 ≤ 3 ≤ 3 ≤ 2

mean = (a + b + c + d)/4

mean = (8 + 3 + 3 + 2)/4

mean = 16/4

mean = 4

range = a - d

range = 8 - 2

range = 6

Answer:

choice a....625 = [tex]5^{4}[/tex] in exponential form

Step-by-step explanation:

625 = 25*25 =  [tex]25^{2}[/tex]  =  [tex]5^{4}[/tex]

Answer:

choice A well be correct !! (did it on usa test prep)

Step-by-step explanation:

Answer:

D) 4

Step-by-step explanation:

4x + 24 = 8x + 2x

adding like terms

4x + 24 = 10x

isolate x now

4x+24-4x = 10-4x

24 = 6x

24/6 = 6x/6

4 = x

D) 4

check our answer by plugging solution into equation

4(4) + 24 = 8(4) + 2(4)

16 + 24 = 32 + 8

40 = 40

Answer:

a)

i) p(x) = 1.4 s(x)

ii) s(x) = p(x) ÷ 1.4 = [p(x)]/1.4

b)

i) p(x) = [s(x) + 200]

ii) s(x) = [p(x) - 200]

c)

i) p(x) = s(x+4)

ii) s(x) = p(x-4)

Step-by-step explanation:

Complete Question

Each summer Primo Pizza and Pizza Supreme compete to see who has the larger summer profit. Let p(x) represent Primo Pizza's profit (in dollars) x days after June 1. Let s(x) represent Pizza Supreme's profit (in dollars) x days after June 1.

a) Suppose Primo Pizza's profit each day is 1.4 times as large as the profit of Pizza Supreme

i. Write a function formula for p using the function s.

ii. Write a function formula for s using the function p.

b) Suppose Primo Pizza's profit each day is $200 more than the profit of Pizza Supreme.

i) Write a function formula for p using the function s.

ii) Write a function formula for s using the function p.

c) Suppose Primo Pizza's profit on a given day is always the same as the profit of Pizza Supreme's profit 4 days later.

i) Write a function formula for p using the function s.

ii) Write a function formula for s using the function p.

The profits per day for Primo Pizza, x days after June 1 = p(x)

The profits per day for Supreme Pizza, x days after June 1 = s(x)

a) Primo Pizza's profits per day is 1.4 times that of Supreme Pizza's per day.

Primo Pizza's profits per day, x days after June 1 = p(x)

Supreme Pizza's profit per day, x days after June 1 = s(x)

i) p(x) = 1.4 s(x)

ii) s(x) = p(x) ÷ 1.4 = [p(x)]/1.4

b) Primo Pizza profits per day is $200 more than that of Supreme Pizza

Primo Pizza's profits per day, x days after June 1 = p(x)

Supreme Pizza's profit per day, x days after June 1 = s(x)

i) p(x) = [s(x) + 200]

ii) s(x) = [p(x) - 200]

c) Primo Pizza's profit on a given day is always the same as the profit of Pizza Supreme's profit 4 days later.

Primo Pizza's profits per day, x days after June 1 = p(x)

Supreme Pizza's profit per day, x days after June 1 = s(x)

Supreme Pizza's profit per day, 4 days later = s(x+4)

So,

i) p(x) = s(x+4)

ii) This means that Supreme Pizza's profit per day is the same as Primo Pizza's profit per day four days ago.

Primo Pizza's profit per day four days ago = p(x-4)

So,

s(x) = p(x-4)

Hope this Helps!!!

Primo Pizza's profit function p(x) is related to Pizza Supreme's profit function s(x) such that p(x) = s(x + 4). Similarly, s(x) = p(x - 4). These functions express the profits in terms of each other with a 4-day shift in time.

Given that Primo Pizza's profit p(x) on a given day is the same as Pizza Supreme's profit s(x) 4 days later, we can write the following relationships between the two functions:

p(x) = s(x + 4)

s(x) = p(x - 4)

This implies that to find Primo Pizza's profit on the x-th day, we need to find out what Pizza Supreme's profit was on the (x + 4)-th day. Conversely, to compute Pizza Supreme's profit on the x-th day, we need to find Primo Pizza's profit 4 days earlier, on the (x - 4)-th day.

Answer:

1 hour 15 Minutes

Step-by-step explanation:

The glider begins its flight [tex]\dfrac{3}{4}[/tex] mile above the ground.

Distance above the ground after 45 minutes =[tex]\frac{3}{10} \:mile[/tex]

Change in height of the glider

[tex]=\frac{3}{4}-\frac{3}{10} \\\\=\frac{15-6}{20}\\\\=\frac{9}{20} miles[/tex]

Next, we determine how long the entire descent last.

Expressing the distance moved as a ratio of time taken

[tex]\frac{9}{20} \:miles : 45 \:minutes\\\\\frac{3}{10}\:miles:x \:minutes\\\\x=45X\frac{3}{10}\div\frac{9}{20} =30 Minutes[/tex]

Therefore: Total Time taken =45+30=75 Minutes

=1 hour 15 Minutes

Step-by-step explanation:

A bag contains 23 coins, some dimes and some quarters. The total amount of money in the bag is $2.75.

Let d be the  number of dimes

and q be the number of quarters

Total cons = 23

so equation becomes

[tex]d+q= 23\\[/tex]

[tex]q=23-d[/tex]

1 dime = 10 cents

and 1 quarter =25 cents

The total amount of money in the bag is $2.75

2.75= 275 cents

[tex]10d+25q=275[/tex]

solve the equation for d  and q

Plug in [tex]q=23-d[/tex] for q in second equation

[tex]10d+25q=275\\10d+25(23-d)=275\\10d+575-25d=275\\[/tex]

combine like terms and subtract 575 from both sides

[tex]10d+575-25d=275\\-15d=275-575\\-15d=-300\\[/tex]

divide both sides by -15

d=20

so the number of dimes = 20

[tex]q=23-d\\q=23-20\\q=3[/tex]

Number of quarter = 3

Answer:

20 dimes

3 quarters

Answer:

27.76% probability that a randomly selected bag of this size has 10 or more green candies

Step-by-step explanation:

I am going to use the normal approximation to the binomial to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 40, p = 0.2[/tex]

So

[tex]\mu = E(X) = np = 40*0.2 = 8[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{40*0.2*0.8} = 2.53[/tex]

What is the probability that a randomly selected bag of this size has 10 or more green candies

Using continuity correction, this is [tex]P(X \geq 10 - 0.5) = P(X \geq 9.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 9.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{9.5 - 8}{2.53}[/tex]

[tex]Z = 0.59[/tex]

[tex]Z = 0.59[/tex] has a pvalue of 0.7224

1 - 0.7224 = 0.2776

27.76% probability that a randomly selected bag of this size has 10 or more green candies

Answer:

[tex]P(x\geq 10)=0.2682[/tex]

Step-by-step explanation:

The number x of green candies in a bag of 40 candies follows a binomial distribution, because we have:

So, the probability that in a bag of 40 candies, x are green is calculated as:

[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]

Replacing, n by 40 and p by 0.2, we get:

[tex]P(x)=\frac{40!}{x!(40-x)!}*0.2^{x}*(1-0.2)^{40-x}[/tex]

So, the probability that a randomly selected bag of this size has 10 or more green candies is equal to:

[tex]P(x\geq 10)=P(10)+P(11)+...+P(40)\\P(x\geq 10)=1-P(x<10)[/tex]

Where [tex]P(x<10)=P(0)+P(1)+P(2)+P(3)+P(4)+P(5)+P(6)+P(7)+P(8)+P(9)[/tex]

So, we can calculated P(0) and P(1) as:

[tex]P(0)=\frac{40!}{0!(40-0)!}*0.2^{0}*(1-0.2)^{40-0}=0.00013\\P(1)=\frac{40!}{1!(40-1)!}*0.2^{1}*(1-0.2)^{40-1}=0.00133[/tex]

At the same way, we can calculated P(2), P(3), P(4), P(5), P(6), P(7), P(8) and P(9) and get that P(x<10) is equal to:

[tex]P(x<10)=0.7318[/tex]

Finally, the probability [tex]P(x\geq 10)[/tex] that a randomly selected bag of this size has 10 or more green candies is:

[tex]P(x\geq 10)=1-P(x<10)\\P(x\geq 10)=1-0.7318\\P(x\geq 10)=0.2682[/tex]

Answer:

a)Null hypothesis:[tex]p\leq 0.14[/tex]  

Alternative hypothesis:[tex]p > 0.14[/tex]  

b) For this case we are conducting a right tailed test so then we need to look in the normal standard distribution a quantile that accumulates 0.01 of the are in the left and we got;

[tex]z_{crit} = 2.33[/tex]

So then the rejection region would be [tex](2.33 , \infty)[/tex]

c) The significance level provided [tex]\alpha=0.01[/tex]. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>2.52)=0.006[/tex]  

And since the p value is lower than the significance level then we can reject the null hypothesis. So then we can conclude that the true proportion of interest is higher than 0.14 at 1% of significance.

Step-by-step explanation:

Data given and notation

n=590 represent the random sample taken

X=104 represent the drivers were wearing their seat belts

We can estimate the sample proportion like this:

[tex]\hat p=\frac{104}{590}=0.176[/tex] estimated proportion of  drivers were wearing their seat belts

[tex]p_o=0.14[/tex] is the value that we want to test

[tex]\alpha=0.01[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

[tex]p_v[/tex] represent the p value (variable of interest)  

a) System of hypothesis

We need to conduct a hypothesis in order to test the claim that the true proportion of drivers were wearing their seat belts is higher than 0.14 or no, so the system of hypothesis are.:  

Null hypothesis:[tex]p\leq 0.14[/tex]  

Alternative hypothesis:[tex]p > 0.14[/tex]  

Part b

For this case we are conducting a right tailed test so then we need to look in the normal standard distribution a quantile that accumulates 0.01 of the are in the left and we got;

[tex]z_{crit} = 2.33[/tex]

So then the rejection region would be [tex](2.33 , \infty)[/tex]

Part c

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z=\frac{0.176 -0.14}{\sqrt{\frac{0.14(1-0.14)}{590}}}=2.52[/tex]  

Statistical decision  

The significance level provided [tex]\alpha=0.01[/tex]. The next step would be calculate the p value for this test.  

Since is a right tailed test the p value would be:  

[tex]p_v =P(z>2.52)=0.006[/tex]  

And since the p value is lower than the significance level then we can reject the null hypothesis. So then we can conclude that the true proportion of interest is higher than 0.14 at 1% of significance.

Answer:

See explanation

Step-by-step explanation:

Solution:-

- Let the proportion of drivers who use a seat belt in a country that does not have a mandatory seat belt law = p.

- A claim was made that p = 0.14. We will state our hypothesis:

                Null hypothesis: p = 0.14

- Two months after the campaign, y = 104 out of a random sample of n = 590 drivers were wearing their seat belts. The sample proportion can be determined as:

               Sample proportion ( p^ ) = y / n = 104 / 590 = 0.176

- The alternate hypothesis will be defined by a population proportion that supports an increase. So we state the hypothesis:

               Alternate hypothesis: p > 0.14

- The rejection is defined by the significance level ( α = 0.01 ). The rejection region is defined by upper tail of standard normal.

- The Z-critical value that limits the rejection region is defined as:

                            P ( Z < Z-critical ) = 1 - 0.01 = 0.99

                            Z-critical = 2.33

- All values over Z-critical are rejected.

- Determine the test statistics by first determining the population standard deviation ( σ ):

- Estimate σ using the given formula:

                      σ = [tex]\sqrt{\frac{p*(1-p)}{n} } = \sqrt{\frac{0.14*(1-0.14)}{590} }= 0.01428[/tex]

- The Z-test statistics is now evaluated:

                     Z-test = ( p^ - p ) / σ

                     Z-test = ( 0.1763 - 0.14 ) / 0.01428

                    Z-test = 2.542

- The Z-test is compared whether it lies in the list of values from rejection region.

                     2.542 > 2.33

                     Z-test > Z-critical

Hence,

                     Null hypothesis is rejected

- The claim made over the effectiveness of campaign is statistically correct.

Answer:

150

Step-by-step explanation:

Two tangents to the circle (until the point where the tangent and circle touch) has the same length, therefore, AR=AT, RG=GE, EN=NT

Then just add up everything!

The 95% confidence interval for the difference in mean concentration between people who have eaten fast food and those who haven't is approximately  16.6  to  32.4  ng/mL.

To find the 95% confidence interval for the difference in mean concentration between people who have eaten fast food and those who haven't, we can use the formula for the confidence interval for the difference between two means:

[tex]\[ \text{CI} = (\bar{X}_1 - \bar{X}_2) \pm Z \times \sqrt{\frac{{S_1^2}}{{n_1}} + \frac{{S_2^2}}{{n_2}}} \][/tex]

Where:

[tex]\( \bar{X}_1 \) and \( \bar{X}_2 \)[/tex] are the sample means of the two groups.

[tex]\( S_1 \) and \( S_2 \)[/tex] are the sample standard deviations of the two groups.

[tex]\( n_1 \) and \( n_2 \)[/tex] are the sample sizes of the two groups.

Z is the critical value from the standard normal distribution for the desired confidence level.

Given:

[tex]\( \bar{X}_1 = 83.6 \)[/tex] (mean concentration of DEHP for people who have eaten fast food)

[tex]\( S_1 = 194.7 \)[/tex] (standard deviation of DEHP for people who have eaten fast food)

[tex]\( n_1 = 3095 \)[/tex] (sample size of people who have eaten fast food)

[tex]\( \bar{X}_2 = 59.1 \)[/tex] (mean concentration of DEHP for people who haven't eaten fast food)

[tex]\( S_2 = 152.1 \)[/tex] (standard deviation of DEHP for people who haven't eaten fast food)

[tex]\( n_2 = 5782 \)[/tex] (sample size of people who haven't eaten fast food)

First, we need to calculate the standard error of the difference in means:

[tex]\[ SE = \sqrt{\frac{{S_1^2}}{{n_1}} + \frac{{S_2^2}}{{n_2}}} \][/tex]

Then, we'll find the critical value Z for a 95% confidence interval, which corresponds to  Z = 1.96  for a two-tailed test.

Finally, we'll plug in the values to calculate the confidence interval.

Let's do the calculations:

First, let's calculate the standard error of the difference in means:

[tex]\[ SE = \sqrt{\frac{{194.7^2}}{{3095}} + \frac{{152.1^2}}{{5782}}} \]\[ SE \approx \sqrt{\frac{{37936.09}}{{3095}} + \frac{{23131.41}}{{5782}}} \]\[ SE \approx \sqrt{12.2604 + 4.0006} \]\[ SE \approx \sqrt{16.261} \]\[ SE \approx 4.032 \][/tex]

Now, we'll find the critical value  Z  for a 95% confidence interval, which corresponds to  Z = 1.96  for a two-tailed test.

Finally, we'll calculate the confidence interval:

[tex]\[ \text{CI} = (83.6 - 59.1) \pm 1.96 \times 4.032 \]\[ \text{CI} = 24.5 \pm 1.96 \times 4.032 \]\[ \text{CI} = 24.5 \pm 7.9072 \][/tex]

Now, let's find the bounds of the confidence interval:

Upper Bound:  24.5 + 7.9072 = 32.4072

Lower Bound:  24.5 - 7.9072 = 16.5928

Rounded to one decimal place, the 95% confidence interval for the difference in mean concentration between people who have eaten fast food and those who haven't is approximately  16.6  to  32.4  ng/mL.

Question :

Is Fast Food Messing With Your Hormones? Examine the results of a study investigating whether fast food consumption increases one's concentration of phthalates, an ingredient in plastics which has been linked to multiple health problems including hormone disruption. The study included 8877 people who recorded all the food they ate over a 24-hour period and then provided a urine sample. Two specific phthalate byproducts were measured (in ng/mL) in the urine: DEHP and DiNP. Find a 95% confidence interval for the difference, HlF MN, in mean concentration between people who have eaten fast food in the last 24 hours and those who haven't. The mean concentration of DEHP in the 3095 participants who had eaten fast food was XF = 83.6 with SF = 194.7, while the mean for the 5782 participants who had not eaten fast food was TN = 59.1 with SN = 152.1. Round your answers to one decimal place: The 95% confidence interval is ______ to _________.

The 95% confidence interval is 16.6 ng/mL to 32.4 ng/mL.

To find the 95% confidence interval for the difference in mean concentration of DEHP between people who have eaten fast food in the last 24 hours and those who haven't, we use the formula for the confidence interval of the difference between two means with unequal variances (often referred to as Welch's t-test).

Given:

Mean concentration for fast food consumers [tex](\( \bar{X}_F \))[/tex] = 83.6 ng/mL

- Standard deviation for fast food consumers [tex](\( S_F \))[/tex] = 194.7 ng/mL

- Sample size for fast food consumers [tex](\( n_F \))[/tex] = 3095

- Mean concentration for non-fast food consumers [tex](\( \bar{X}_N \))[/tex] = 59.1 ng/mL

- Standard deviation for non-fast food consumers [tex](\( S_N \))[/tex] = 152.1 ng/mL

- Sample size for non-fast food consumers [tex](\( n_N \))[/tex] = 5782

The formula for the 95% confidence interval for the difference in means [tex](\( \mu_F - \mu_N \))[/tex] is:

[tex]\[ (\bar{X}_F - \bar{X}_N) \pm t^* \sqrt{\frac{S_F^2}{n_F} + \frac{S_N^2}{n_N}} \][/tex]

First, we calculate the standard error (SE):

[tex]\[ SE = \sqrt{\frac{S_F^2}{n_F} + \frac{S_N^2}{n_N}} \][/tex]

Plugging in the values:

[tex]\[ SE = \sqrt{\frac{194.7^2}{3095} + \frac{152.1^2}{5782}} \]\[ SE = \sqrt{\frac{37926.09}{3095} + \frac{23133.41}{5782}} \]\[ SE = \sqrt{12.253 + 4.001} \]\[ SE = \sqrt{16.254} \]\[ SE = 4.03 \][/tex]

Next, we find the degrees of freedom (df) using the formula for Welch's t-test:

[tex]\[ df \approx \frac{\left( \frac{S_F^2}{n_F} + \frac{S_N^2}{n_N} \right)^2}{\frac{\left( \frac{S_F^2}{n_F} \right)^2}{n_F-1} + \frac{\left( \frac{S_N^2}{n_N} \right)^2}{n_N-1}} \]\[ df \approx \frac{\left( 12.253 + 4.001 \right)^2}{\frac{12.253^2}{3094} + \frac{4.001^2}{5781}} \]\[ df \approx \frac{16.254^2}{\frac{150.13}{3094} + \frac{16.008}{5781}} \]\[ df \approx \frac{264.188}{0.0485 + 0.0028} \]\[ df \approx \frac{264.188}{0.0513} \]\[ df \approx 5149 \][/tex]

For a large [tex]\( df \), the \( t^* \)[/tex] value for a 95% confidence interval is approximately 1.96.

Now, we can calculate the confidence interval:

[tex]\[ (\bar{X}_F - \bar{X}_N) \pm t^* \cdot SE \]\[ (83.6 - 59.1) \pm 1.96 \cdot 4.03 \]\[ 24.5 \pm 7.9 \][/tex]

So, the 95% confidence interval for the difference in mean concentration of DEHP between people who have eaten fast food in the last 24 hours and those who haven't is:

[tex]\[ 16.6 \text{ to } 32.4 \][/tex]

The 95% confidence interval is 16.6 to 32.4 ng/mL.

Complete  question- Is Fast Food Messing With Your Hormones? Examine the results of a study investigating whether fast food consumption increases one's concentration of phthalates, an ingredient in plastics which has been linked to multiple health problems including hormone disruption. The study included 8877 people who recorded all the food they ate over a 24-hour period and then provided a urine sample. Two specific phthalate byproducts were measured (in ng/mL) in the urine: DEHP and DiNP. Find a 95% confidence interval for the difference, HlF MN, in mean concentration between people who have eaten fast food in the last 24 hours and those who haven't. The mean concentration of DEHP in the 3095 participants who had eaten fast food was XF = 83.6 with SF = 194.7, while the mean for the 5782 participants who had not eaten fast food was TN = 59.1 with SN = 152.1. Round your answers to one decimal place: The 95% confidence interval is ______ to _________.

Answer:

C. x = 3cm

Step-by-step explanation:

The formula for volume of a triangular prism is

V = base * height

x in this case equals height, and the base is the area of the triangular base, which is

A(triangle) = 1/2 b*h

                 = 1/2 7*10 = 35 square centimeters

Plug this back into our formula:

V = base * height

105 = 35x

Solve for x.

105/35 = x

C. x = 3 cm

Answer:

C. 3 cm

Step-by-step explanation:

The volume of a triangular prism is denoted by: [tex]V=Bh[/tex], where B is the base area and h is the height.

Here, the base is actually the triangle, and we can calculate this area by using the formula for a triangle's area: [tex]A=\frac{1}{2} bh[/tex]. Here, b = 10 and h = 7, so:

[tex]A=\frac{1}{2} bh[/tex]

[tex]A=\frac{1}{2} *10*7=5*7=35[/tex] cm squared

Now, the height of the prism is x and we already know the volume is 105, so plug these values in:

[tex]V=Bh[/tex]

[tex]105=35*x[/tex]

x = 105/35 = 3

The answer is C.

Answer:

There is no relationship between voles and food preference (The food preferences among vole species are independent of one another)

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. The null hypothesis tries to establish that the old theory is true. So, for the case above, the old theory is that there is no relationship between voles species and food preference which is the null hypothesis.

The null hypothesis in Dr. Pagels' study is that there is no difference in the food preferences for peanut butter-oatmeal mixture and apple slices between meadow and common voles.

In the study conducted by Dr. Pagels for determining the food preference of meadow and common voles, the null hypothesis posits that there is no difference in preference for the peanut butter-oatmeal mixture or apple slices between the two species of voles. This implies that both meadow and common voles would choose either food option at an equal rate, suggesting that any observed preference could be attributed to random chance rather than a true preference.

The purpose of the null hypothesis is to establish a baseline expectation that no effect or difference is present, which can then be challenged by the experimental data. If significant differences in the vole populations' food choices are observed, the null hypothesis may be rejected, pointing to a potential preference for one food type over the other among the different vole species.

Answer: 21 quarts. Annie will need a total of 21 quarts of coffee.

Step-by-step explanation: 16 fl oz = 0.5 quarts. 0.5 * 42 =21

21 quartz of coffee needed to 42 mugs.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Capacity of Coffee mug= 16 fluid ounce

1 fluid ounce = 0.03125 liquid quartz

16 fluid ounce = 16 x 0.03125

                       = 0.5 quartz

So, for 42 mugs the amount coffee needed

= 42 x 0.5

= 21 quartz

Hence, 21 quartz of coffee needed to 42 mugs.

Learn more about unitary method here:

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The cars should be rented at a rate of $30 per day to produce the maximum income of $13200 per day.

To solve this problem, we can use the following steps:

Define the variables.

Let x be the number of cars rented per day and y be the rate per day.

Write down the equation for the revenue.

The revenue is equal to the number of cars rented multiplied by the rate per day. Therefore, the equation for the revenue is:

R = x * y

Write down the equation for the decrease in demand. For each $1 increase in rate, 10 fewer cars are rented. Therefore, the equation for the decrease in demand is:

D = -10 * (y - 30)

Set the revenue equal to the maximum value. The revenue is maximized when the derivative of the revenue function is zero. Therefore, we set the derivative of the revenue function equal to zero and solve for y.

R' = x = 0

x = 440

y = 30

Calculate the maximum revenue. The maximum revenue is equal to the number of cars rented multiplied by the rate per day. Therefore, the maximum revenue is:

R = 440 * 30 = $13200

Therefore, the cars should be rented at a rate of $30 per day to produce the maximum income of $13200 per day.

For such more question on income

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Answer:

-8/7

Step-by-step explanation:

Answer:

Guido stayed in US in 2018 for 180 days which are greater than 31 days.

Guido Stayed in US in 2018 and in 2017 = (180 + 66) > 183 days.

So, yes Guido does meet US Statutory definition in 2018 and stayed 180 days in 2018.  

Step-by-step explanation:

Let's find out how many days in total Guido stayed in US in these 3 years 2017, 2018 and 2019.

Year = 2017

Days = 200

Year = 2018

Days = 180

Year = 2019

Days = 70

Total days stayed = 200 + 180 + 70

Total Days Stayed = 450 days.

In U.S, there are two tests are in place and for non-citizen of U.S and for the resident Alien or non - resident Alien status, one must pass one of these two tests, which are as follows:

1. Green Card Test:

2. Substantial Presence Test:

Here, in this problem, Guido is citizen and resident of Belgium. So, will check his criteria according to the substantial presence test.

So, the question is: how many days Guido was present in the U.S in 2018 under resident alien status.

In 2018, Guido stayed in US for 180 days.

So, according to the Substantial Presence test, one must be physically present in US for more than 31 days to be eligible for resident alien status. In addition, in 2018, his total of physical presence in US in 2018 and one third of physical presence in 2017 must be greater than 183 days.

If we see, both conditions are matched in case of Guido.

Guido stayed in US in 2018 for 180 days which are greater than 31 days.

Guido Stayed in US in 2018 and in 2017 = (180 + 66) > 183 days.

So, yes Guido does meet US Statutory definition in 2018 and stayed 180 days in 2018.  

Final answer:

In 2018, Guido was present in the United States for a total of 180 days according to the substantial presence test for determining resident alien status for tax purposes.

Explanation:

Under the substantial presence test, which is used to determine if an individual is a resident alien for tax purposes in the United States, only the days present in the current year (which, in the scenario provided, is 2018) are counted in full. In this case, Guido was present in the U.S. for 180 days in 2018. Days from prior years are counted partially, with only 1/3 of the days in the first preceding year and 1/6 of the days from the second preceding year included in the calculation. However, when determining how many days were present in a given year, such as 2018 in this example, only the days in that specific year are relevant. Therefore, according to the substantial presence test, in 2018, Guido was present in the United States for a total of 180 days.

Answer:

99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Step-by-step explanation:

We are given that a high school principal wishes to estimate how well his students are doing in math.

Using 40 randomly chosen tests, he finds that 77% of them received a passing grade.

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

                          P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of students received a passing grade = 77%

           n = sample of tests = 40

           p = population proportion

Here for constructing 99% confidence interval we have used One-sample z proportion test statistics.

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99  {As the critical value of z at 0.5%

                                           level of significance are -2.5758 & 2.5758}  

P(-2.5758 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.5758) = 0.99

P( [tex]-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

P( [tex]\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

99% confidence interval for p = [[tex]\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]

 = [ [tex]0.77-2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } }[/tex] , [tex]0.77+2.5758 \times {\sqrt{\frac{0.77(1-0.77)}{40} } }[/tex] ]

 = [0.5986 , 0.9414]

Therefore, 99% confidence interval for the population proportion of passing test scores is [0.5986 , 0.9414].

Lower bound of interval = 0.5986

Upper bound of interval = 0.9414

Answer:

Approximately = 20.0 inch to the nearest tenth

Step-by-step explanation:

We are going to calculate this by using the formula of the circle in a way.

Radius = 6 inches

Now between 10:25 a.m. and 11:00 a.m , the minute hand moved 35 minutes.

But there are total of 60 minutes in the clock which makes it a complete circle.

So 60 minutes = 2π

35 minutes = ?.

35 minutes =( 35*2π)/60

35 minutes = 1.166667π

So the distance covered by the minute hand = 1.166667π * 6 inches

= 21.991 inches

Approximately = 20.0 inch to the nearest tenth