Answer:
We conclude that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.
Step-by-step explanation:
We are given that a survey of 2,254 American adults indicates that 17% of cell phone owners browse the internet exclusively on their phone rather than a computer or other device. According to an online article, a report from a mobile research company indicates that 38 percent of Chinese mobile web users only access the internet through their cell phones.
We have to conduct a hypothesis test to determine if these data provide strong evidence that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.
Let p = proportion of Americans who only use their cell phones to access the internet
SO, Null Hypothesis, [tex]H_0[/tex] : p = 38% {means that the proportion of Americans who only use their cell phones to access the internet is same as that of Chinese proportion of 38%}
Alternate Hypothesis, [tex]H_a[/tex] : p [tex]\neq[/tex] 38% {means that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%}
The test statistics that will be used here is One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1- \hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = proportion of cell phone owners who browse the internet
exclusively on their phone in a survey of 2,254 adults = 17%
n = sample of adults = 2,254
So, test statistics = [tex]\frac{0.17-0.38}{\sqrt{\frac{0.17(1- 0.17)}{2,254} } }[/tex]
= -26.542
Since in the question we are not given with the significance level so we assume it to be 5%. So, at 0.05 level of significance, the z table gives critical values between -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie in between the critical values of z so we have sufficient evidence to reject null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the proportion of Americans who only use their cell phones to access the internet is different than the Chinese proportion of 38%.
which property of addition is used in the following (7+9)+5=7+(9+5)
Answer:
associative property of addition
Step-by-step explanation:
The 5 is substituted into the parentheses and the 7 is taken out.
A clinical trial tests a method designed to increase the probability of conceiving a girl. In the study 425 babies were born, and 340 of them were girls. Use the sample data to construct a 99% confidence interval estimate of the percentage of girls born. Based on the result, does the method appear to be effective? 0.75less than pless than 0.85 (Round to three decimal places as needed.) Does the method appear to be effective? No, the proportion of girls is not significantly different from 0.5. Yes, the proportion of girls is significantly different from 0.5.
Answer:
0.75<p<0.85
Yes,the proportion of girls is significantly different from 0.5.
Step-by-step explanation:
We calculate the proportion of girls:
[tex]p=\frac{340}{425}\\\\\\\\=0.8[/tex]
#We then calculate the confidence interval as follows:
[tex]CI=p\pm z(ME)\\\\=p\pm z_{0.005}\sqrt{\frac{p(1-p)}{n}}\\\\=0.8+2.576\times \sqrt{\frac{0.8\times 0.2}{425}}\\\\=0.8\pm0.05\\\\=[0.75,0.85][/tex]
Hence, the proportion's confidence interval at 99% is 0.75<p<0.85
#We then state our hypothesis to validate the claim:
[tex]H_o:p=0.5\\H_a:p>0.5\\\\p=0.8(True \ mean)[/tex]
Since the confidence interval does not contain 0.5, which is the the 50% chance of having a girl, then it can be concluded the proportion of girls is significantly different from 0.5.
Tony buys a pair of running shoes f 80$ he pays 9%sales tax how much does the pair of shoes cost in total?
an eggseller charged Mrs ada#1450 for 100 eggs . how much did she pay for each egg
Answer:
14.5
step by step explanation:
1450÷100= 14.5
Final answer:
Mrs. Ada paid #14.50 for each egg after being charged #1450 for 100 eggs. This is calculated by dividing the total cost by the number of eggs.
Explanation:
To calculate the cost of each egg when Mrs. Ada charged #1450 for 100 eggs, we need to divide the total cost by the number of eggs. This is a simple division problem under the subject of mathematics.
The formula to find the cost per egg is:
Total cost of eggs ÷ Number of eggs = Cost per egg
#1450 ÷ 100 eggs = #14.50 per egg
Therefore, Mrs. Ada paid #14.50 for each egg.
The high price of medicines is a source of major expense for those seniors in the United States who have to pay for these medicines themselves. A random sample of 1800 seniors who pay for their medicines showed that they spent an average of $ 4600 last year on medicines with a standard deviation of $ 800 . Make a 90 % confidence interval for the corresponding population mean.
Answer:
[tex]4600-1.646\frac{800}{\sqrt{1800}}=4568.96[/tex]
[tex]4600+1.646\frac{800}{\sqrt{1800}}=4631.04[/tex]
We are confident at 90% that the true mean for the amount spent on medicines is between (4568.96 and 4631.04)
Step-by-step explanation:
Information given
[tex]\bar X=4600[/tex] represent the sample mean for the amount spent on medicines
[tex]\mu[/tex] population mean
s=800 represent the sample standard deviation
n=1800 represent the sample size
Solution
The confidence interval for the true population mean is given by:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
We can calculate the degrees of freedom with:
[tex]df=n-1=1800-1=1799[/tex]
We know that the Confidence level is 0.90 or 90%, the value of significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.05,1799)".And we see that [tex]t_{\alpha/2}=1.646[/tex]
Replcing in the formula for the confidence interval we got:
[tex]4600-1.646\frac{800}{\sqrt{1800}}=4568.96[/tex]
[tex]4600+1.646\frac{800}{\sqrt{1800}}=4631.04[/tex]
We are confident at 90% that the true mean for the amount spent on medicines is between (4568.96 and 4631.04)
Find the circumference of the circle.Use 3.14 pi
Looks like pizza
13in
Answer:
do you know your radius or diameter?
A square-based prism made of clay had dimensions of 6 by 6 by 10. A pyramid was removed from the prism so the prism has no top. what is the total surface area of the remaining clay solid if the slant height of the pyramid is 10.5
Answer:
Step-by-step explanation:
Given that,
The square based prism has dimensions is
6 by 6 by 10
Length = 6
Width = 6
Height = 10
Slant height of pyramid is given as
h = 10.6
Note: The base of the pyramid matches the top of the square prism, so it's square-based prism.
So, we are going to have
4 rectangular faces(i.e the square Base prism rectangular faces)
1 square face ( the based of the prism)
four triangular faces( the top pyramid)
So, area of the four face
It is a rectangular shape and it is calculated using
A = length × Breadth
Area of one face is
A = L × W
A = 6 × 10 = 60 Square units
And there are 4 similar rectangle
So, area of the four rectangles is
A' = 4 × 60 = 240 square unit
Now, area of the square base below can be calculated using
A = s²
A" = L² = 6² = 36 Square units
Now, area of the four triangle pyramid at the top
Area of triangle is given as
A = ½bh
A = ½ × 6 × 10.6
A = 31.8 square units.
The area of the four triangles becomes
A"' = 4 × 31.8
A"' = 126 square units
Then, the total area of the shape is
A(total ) = A' + A" + A"'
A(total) = 240 + 36 + 126
A(total) = 402 Square units
So, the total area of the solid shape is 402 Square units
a) A standard deck consists of 52 cards. Four of the cards are aces. Twenty-six of the cards are red. A poker hand consists of 5 cards dealt at random from the deck. Without calculation, say which has the bigger SD and explain why: the number of aces in the poker hand the number of red cards in the poker hand b) Use a code cell to find the numerical values of the SDs
Answer:
a)The number of aces in the poker hand is greater
b)It is about[tex]\sqrt{2}[/tex] as accurate.
I need help for this question because I need to understand this topic!
You and your family decide to go on a camping trip. As long as it stays above 58°F, your baby brother will get to come along. The function T(x) represents the temperature in degrees Fahrenheit, where x is the number of hours you are at the campsite. It is supposed to be the coldest 3 hours after you arrive. Use T(x) = x4 – 2x3 + x2 + 27 to determine the lowest temperature tonight. Will your brother get to go on the trip?
Answer:
yes, brother can go
Step-by-step explanation:
Apparently, you're not to think to deeply about this function. Rather, you are to take the question at face value. It is asking if the value of T(3) is more than 58.
Evaluation of polynomials is facilitated by writing them in "Horner form."
T(x) = ((x -2)x +1)x^2 +27
T(3) = ((3 -2)3 +1)9 +27 = (3 +1)9 +27 = 36 +27
T(3) = 63
The coldest temperature is supposed to be 63 degrees, which is above 58 degrees. Baby brother can come along.
Answer:
yes, the little brother can go
Step-by-step explanation:
the lowest will be 63 degrees so the baby can go
Which statements are true about the solution of 15>22+x? Select three options.
Answer:
The answer is B, C, and E
Step-by-step explanation:
I hope this helps have a nice day! ❤
Sixty percent of the customers of a fast food chain order the Whopper, french fries and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that EXACTLY 10 will show that the above three food items were ordered
Answer:
18.59% probability that EXACTLY 10 will show that the above three food items were ordered
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they order the above food items, or they do not. The probability of a customer ordering these items is independent of other customers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Sixty percent of the customers of a fast food chain order the Whopper, french fries and a drink.
This means that [tex]p = 0.6[/tex]
If a random sample of 15 cash register receipts is selected, what is the probability that EXACTLY 10 will show that the above three food items were ordered
This is P(X = 10) when n = 15. So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 10) = C_{15,10}.(0.6)^{10}.(0.4)^{5} = 0.1859[/tex]
18.59% probability that EXACTLY 10 will show that the above three food items were ordered
Little Book LTD has total assets of $860 000. There are 75 000 shares of stock outstanding, total book value of $750 000 with a market value of $12 a share. The firm has a profit margin of 6.5% and a total asset turnover of 1.5.
a) Calculate the company’s EPS?
b) What is the market –to- book ratio?
a) Little book LTD earning per share is $1.118 per share.
Explanation:
To calculate earning per share we will use following formula:[tex]\frac{NET INCOME}{WEIGHTED AVERAGE SHARE OUTSTANDING}[/tex]
Now to find net income we will take help of asset turnover ratio :[tex]\frac{NET SALES}{TOTAL ASSET}[/tex]
NOTE : LET x BE THE NET SALES DURING THE YEAR.
Asset turnover ratio = [tex]\frac{x}{860000}[/tex]
1.5 × $860000 = x
x (net sales) = $1290000
Outstanding shares = 75000 shares
So Net Income = $1290000×.065
= $83850
Now Earning per share = [tex]\frac{83850}{75000}[/tex]
Earning per share = $1.118
b) Market to Book Ratio will be 1.2 for Little Book LTD.
Explanation:
Market to Book Ratio =[tex]\frac{MARKET CAPITALIZATION}{TOTAL BOOK VALUE}[/tex]
Market Capitalization = $ 75000× $ 12
= $900000
So, Market To Book Ratio =[tex]\frac{900000}{750000}[/tex] = 1.2
So , Market To Book Ratio is 1.2 for little book ltd.
Anwer question bellow
Answer:
C) y=4x-12.5
Step-by-step explanation:
8x-2y=25
-2y=25-8x
y=-12.5+4x
y=4x-12.5
Therefore C is the right answer
he one-way ANOVA null hypothesis is rejected when the _________.Multiple Choiceratio of the within-treatments variance and the between-treatments variance is 1variability in the sample means can be explained by chanceratio of the within-treatments variance and the between-treatments variance is signficialy greater than 1two estimates of the variance are relatively close together
Answer: two estimates of the variance are relatively close together
Step-by-step explanation:
a music company signed 12 new artists to its label in 2002. Out of the 12, 10 artists have hit songs. Write a ratio to compare the number of artists with hit songs to the total number of artists signed in 2002.
To compare the number of artists with hit songs to the total number of artists signed, write a ratio using the two numbers. The ratio of artists with hit songs (10) to total artists signed (12) simplifies to 5:6 after dividing by the greatest common factor.
Explanation:The student has asked to write a ratio comparing the number of artists with hit songs to the total number of artists signed by a music company in 2002. To do this, we take the number of artists with hit songs and place it in the numerator (top part) of the ratio and the total number of artists in the denominator (bottom part).
To write the ratio in its simplest form, we divide the numerator and the denominator by their greatest common factor if necessary. In this case, the ratio is already in the simplest form.
Step-by-Step Solution:
Number of artists with hit songs: 10
Total number of artists signed: 12
Write the ratio as 10:12
Simplify the ratio by dividing both numbers by 2, the greatest common factor, to get 5:6
So, the simplified ratio of the number of artists with hit songs to the total number of artists signed is 5:6.
An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:
418 421 422 422 425 429 431 434 437
439 446 447 449 452 457 461 465
Calculate a two-sided 95% confidence interval for true average degree of polymerization. (Round your answers to two decimal places.)
Answer:
[tex]438.53-2.12\frac{14.988}{\sqrt{17}}=430.82[/tex]
[tex]438.53+2.12\frac{14.988}{\sqrt{17}}=446.24[/tex]
So on this case the 95% confidence interval would be given by (430.82;446.24)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
In order to calculate the mean and the sample deviation we can use the following formulas:
[tex]\bar X= \sum_{i=1}^n \frac{x_i}{n}[/tex] (2)
[tex]s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}[/tex] (3)
The mean calculated for this case is [tex]\bar X=438.53[/tex]
The sample deviation calculated [tex]s=14.988[/tex]
In order to calculate the critical value [tex]t_{\alpha/2}[/tex] we need to find first the degrees of freedom, given by:
[tex]df=n-1=17-1=16[/tex]
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,16)".And we see that [tex]t_{\alpha/2}=2.12[/tex]
Now we have everything in order to replace into formula (1):
[tex]438.53-2.12\frac{14.988}{\sqrt{17}}=430.82[/tex]
[tex]438.53+2.12\frac{14.988}{\sqrt{17}}=446.24[/tex]
So on this case the 95% confidence interval would be given by (430.82;446.24)
A survey published in the American Journal of Sports Medicine reported the num- ber of meters (m) per week swum by two groups of swimmers—those who competed exclusively in breaststroke and those who competed in the individual medley (which includes breaststroke). The number of meters per week practicing the breaststroke 1 was recorded for each swimmer, and the summary statistics are given below. Is there sufficient evidence to indicate that the average number of meters per week spent prac- ticing breaststroke is greater for exclusive breaststrokers than it is for those swimming individual medley?
Answer:
see explaination
Step-by-step explanation:
Let mu1 be the mean for exclusively breaststroke
Let mu2 be the mean for individual medley
----------------------------------------------------------------------------------------------------------
(a) H o: mu1=mu2 (i.e. null hypothesis)
Ha: mu1> mu2 (i.e. alternative hypothesis)
----------------------------------------------------------------------------------------------------------
(b) Since both sample sizes are grearter than n=30, we can use normal distriubtion.
It is a one-tailed test.
Given a=0.01, the critical value is Z(0.01) =2.33 (from standard normal table)
So the rejection region is Z>2.33
----------------------------------------------------------------------------------------------------------
(c) The test statistic is
Z=(xbar2-xbar2)/sqrt(s1^2/n1+s2^2/n2)
=(9017-5853)/sqrt(7162^2/130+1961^2/80)
=4.76
----------------------------------------------------------------------------------------------------------
(d) Since Z=4.76 is larger than 2.33, we reject the null hypothesis.
----------------------------------------------------------------------------------------------------------
(e) In conclusion there is sufficient evidence to indicate that the average number of meter per week spent practicing breaststroke is greater for exclusive breaststrokers than it is for those swimming individual medley
There is sufficient evidence to indicate that the mean number of breaststroke is greater for exclusive breaststrokers than for swimming individual medley.
What are null hypotheses and alternative hypotheses?In null hypotheses, there is no relationship between the two phenomena under the assumption that it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.
Let μ₁ be the mean for the exclusive breaststroke.
Let μ₂ be the mean for the individual medley.
For the null hypothesis, we have
H₀: μ₁ = μ₂
For the alternative hypothesis, we have
Hₐ: μ₁ > μ₂
The sample size of both is greater than 30, then the normal distribution will be
a = 0.01
The critical value is z(0.01) = 2.33 (From standard normal table)
So the rejection region is z > 2.33
The test statistic will be
[tex]z = \dfrac{\mu_2 - \mu_1}{\sqrt{s^2_1/n_1 + s^2_2/n_2}}\\\\\\z = \dfrac{9017 - 5853}{\sqrt{7162^2/130+1961^2/80}}\\\\\\z = 4.76[/tex]
Since the value of z is greater than 2.33, then we reject the null hypothesis.
More about the null hypotheses and alternative hypotheses link is given below.
https://brainly.com/question/9504281
A newsletter publisher believes that 49% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.05 level to refute the publisher's claim? State the null and alternative hypotheses for the above scenario.
Answer:
A newsletter publisher believes that 49% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.05 level to refute the publisher's claim? State the null and alternative hypotheses for the above scenario.
Null hypothesis ⇒ H₀: p = 0.49
Alternative hypothesis ⇒ Hₐ: p ≠ 0.49
Step-by-step explanation:
Given that α = 0.05
From the given information, the null and alternative hypothesis is expressed below:
Null hypothesis ⇒ H₀: p = 0.49
Alternative hypothesis ⇒ Hₐ: p ≠ 0.49
It has been determined with 95% confidence that the proportion of on-line students at SPC who live in Pinellas County is between 0.73 and 0.77. Determine the sample proportion of on-line SPC students who live in Pinellas County.
Answer:
sample proportion is 0.75
Step-by-step explanation:
given data
confidence = 95%
Pinellas County between = 0.73 and 0.77
solution
We write confidence interval in terms of p and E as
(p - E ) < P < ( p + E ) ................1
when we compare it 0.73 < p < 0.77
we get
so here
p - E = 0.73 ................2
and E is 0.02 so
p - 0.02 = 0.73
p = 0.75
The sample proportion of on-line SPC students who live in Pinellas County is 0.75.
The sample proportion is the point estimate that lies in the middle of the confidence interval.
To find the sample proportion from the given confidence interval, you calculate the average of the lower and upper bounds.
The lower bound is 0.73, and the upper bound is 0.77.
0.73 + 0.77 = 1.50
1.50 / 2
= 0.75
Therefore, the sample proportion of on-line SPC students who live in Pinellas County is 0.75.
How long is a pipeline that runs diagonally across a square field 6 kilometers on a side?
Answer: the square root of 72 which is approximately 8.5
Step-by-step explanation:
When draw a line diagonally in a square you get 2 right triangles so you can do pathogream theorem on them so a squared plus b squared equals c squared. In this case 6^2 + 6^2 = c^2. By solving you get the answer
The length of the pipeline running diagonally across the square field is 8.485 kilometers.
What is Pythagoras theorem?The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the sides of the square field are each 6 kilometers long. Let's sides of the square as a, b, and c, where c is the length of the diagonal (the pipeline) and a and b are the sides of the square.
Using the Pythagorean theorem, we have:
c² = a² + b²
Since the square field is a square, all sides are equal, so a = b = 6 kilometers.
c² = 6² + 6²
c² = 36+ 36
c² = 72
c = 8.485 Km
Therefore, the length of the pipeline running diagonally across the square field is 8.485 kilometers.
Learn more about Pythagoras Theorem here:
https://brainly.com/question/21926466
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Suppose that qequals30, Lequals5, and Kequals15 is a point on the production function qequalsf(L, K). Is it posssible for qequals30, Lequals5, and Kequals16 to also be a point on this production function? Why or why not? The combination qequals30, Lequals5, and Kequals16
Answer:
No
Step-by-step explanation:
If q=30, L=5, and K=15 is a point on the production function q=f(L, K).
Production function is an equation that expresses the relationship between the quantities of factors of production used and the amount of product obtained under the assumption that the most efficient available methods of production are used.
The combination q=30, L=5, and K=16 cannot be a point because we assume production functions are efficient.
Answer:
option E is correct which states that cannot be a point because we assume production functions are efficient.
It is believed that as many as 23% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. Question 1. How many of this younger age group must we survey in order to estimate the proportion of non-grads to within .10 with 90% confidence
Answer: here are 48 adults of this younger age group.
Step-by-step explanation:
Since we have given that
Error = 0.10
p = 23% = 0.23
At 90% level of significance, i.e. α = 0.10
So, the value of z = 1.645
[tex]n=(\dfrac{z}{E})^2p(1-p)\\\\n=(\dfrac{1.645}{0.1})^2(0.23)(1-0.23)\\\\n=270.6025\times 0.23\times 0.77\\\\n=47.92\\\\n\approx 48[/tex]
Hence, there are 48 adults of this younger age group.
Research at the University of Toledo indicates that 50 percent ofthe students change their major area of study after their firstyear in a program. A random sample of 100 students in the Collegeof Business revealed that 48 had changed their major area of studyafter their first year of the program.Has there been a significant decrease in the proportion of studentswho change their major after the first year in this program? Testat the .05 level of significance.(a) What is the decisionrule? (Round youranswer to 3 decimal places.)(b) The value ofthe test statistic is . (Roundyour answer to 2 decimal places.)(c) What is yourdecision regarding ?
Answer:
a) The decision rule is:
Reject the null hypothesis if P-value is under 0.05 (or the test statistic is larger than z=-1.645).
b) Test statistic z=-0.30
c) The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that there has been a significant decrease in the proportion of students who change their major after the first year in this program.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim we have to test is that there has been a significant decrease in the proportion of students who change their major after the first year in this program.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.5\\\\H_a:\pi< 0.5[/tex]
The significance level is α=0.05.
The sample has a size n=100.
The sample proportion is p=0.48.
[tex]p=X/n=48/100=0.48[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{100}}\\\\\\ \sigma_p=\sqrt{0.0025}=0.05[/tex]
We can calculate the test statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.48-0.5+0.5/100}{0.05}=\dfrac{-0.015}{0.05}=-0.3[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z<-0.3)=0.3821[/tex]
The P-value (0.3821) is bigger than the significance level (0.05), then the effect is not significant.
The null hypothesis failed to be rejected.
If we use the critical value approach, the critical value of z for this test with 5% significance level is z=1.645.
There is not enough evidence to support the claim that there has been a significant decrease in the proportion of students who change their major after the first year in this program.
Which is true?
A) 6 inches = 2 feet
B) 6 yards = 2 feet
C) 6 feet = 2 yards
D) 6 feet = 2 inches
Answer:
C.
Step-by-step explanation:
A local grocery store wants to predict its daily sales in dollars. The manager believes that the amount of newspaper advertising significantly affects sales. He randomly selects 7 days of data consisting of daily grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). The Excel/MegaStat output given above summarizes the results of the regression model. What is the value of the simple coefficient of determination?
Answer:
Step-by-step explanation:
Hello!
The manager of the store made a linear regression analysis to study if the amount of newspaper advertising (independent variable, X) significantly affects the sales (dependent variable, Y)
The coefficient of determination R² is a statistic that measures the percentage of the variability of Y that is explained by X in the context of the regression model. It also determines the ability of the model to replicate the results of the analysis.
The Excel output is attached below, the calculated determination coefficient is:
R²= 0.726
Interpretation
72.6% of the variability of the estimated average daily sales of the grocery store is explained by the amount of newspaper advertisement placed under the estimated model.
I hope this helps!
Piecewise and Combining Functions
The hours on a clock face are 30 apart. What is the angle a line from one o'clock to 6 o'clock make with a horizontal line
The angle between a line from 1 o'clock to 6 o'clock and a horizontal line is 150 degrees.
* The clock face has hours spaced 30 degrees apart.
* You want to find the angle between a line from 1 o'clock to 6 o'clock and a horizontal line.
1. **Finding the angle between consecutive hours:** Each hour on the clock face is 30 degrees apart from its neighbors. Therefore, the angle between 1 o'clock and 2 o'clock is 30 degrees, and the angle between 2 o'clock and 3 o'clock is also 30 degrees, and so on.
2. **Calculating the angle from 1 o'clock to 6 o'clock:** To get from 1 o'clock to 6 o'clock, we must move five hour marks counter-clockwise. Since each hour mark represents 30 degrees, moving five marks corresponds to an angle of 5 * 30 degrees = 150 degrees.
Therefore, the angle between a line from 1 o'clock to 6 o'clock and a horizontal line is 150 degrees.
A shipping company is creating their own shipping boxes. They have created a box with a volume of 800in^3, a helght of 8 inches and a base perimeter of 40 inches.
The machine malfunctioned, and in order to be fixed the correct dimensions of the box needed to be input. What length and width would a worker need to input in
order to fix the machine?
Length:?
inches width:?
Answer:
Length=10 Inches
Width=10 Inches
Step-by-step explanation:
Volume of the box [tex]=800in^3[/tex]
Height=8 Inches
Base Perimeter =40 Inches
Volume of a box=lbh
SInce h=8 in, V=800.
Then:
8bl=800
bl=100
[tex]l=\frac{100}{b}[/tex]
Base Perimeter=40 Inches
Perimeter of the Base= 2(l+b)
Therefore: 2(l+b)=40
Substituting [tex]l=\frac{100}{b}[/tex]
[tex]2(\frac{100}{b}+b)=40\\\frac{100+b^2}{b}=20\\$Cross Multiply\\100+b^2=20b\\b^2-20b+100=0\\$Solving the quadratic equation \\b^2-10b-10b+100=0\\b(b-10)-10(b-10)=0\\(b-10)(b-10)=0\\b-10=0 (Twice)\\b=10 \:Inch[/tex]
Recall:
[tex]l=\frac{100}{b}=\frac{100}{10}\\l=10 Inch[/tex]
Therefore:
Length=10 Inches
Width=10 Inches
Complete the work shown to find a possible solution of the equation.
(x-5)1/2+5=2, (x-5)1/2=-3, [(x-5)1/2]=(-3)^2. A possible solution of the equation is
Answer: the answer is 14
Step-by-step explanation:
Answer:
14
Step-by-step explanation:
Correct on edge 2021
A study by Consumer Reports showed that 64% of supermarket shoppers believe supermarket brands to be as good as national name brands. To investigate whether this result applies to its own product, the manufacturer of a national name-brand ketchup asked a sample of shoppers whether they believed that supermarket ketchup was as good as the national brand ketchup.
a. Formulate the hypotheses that could be used to determine whether the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differed from 64%.
b. If a sample of 100 shoppers showed 52 stating that the supermarket brand was as good as the national brand, what is the p-value (to 4 decimals)?
c. At = α= 0.05, what is your conclusion?
d. Should the national brand ketchup manufacturer be pleased with this conclusion?
Answer:
a) As the claim is that the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differs from 64% , the percentage can be significantly highly or lower. Then, the test is two-tailed and the null and alternative hypothesis are:
[tex]H_0: \pi=0.64\\\\H_a:\pi\neq 0.64[/tex]
b) P-value = 0.0166
c) At α= 0.05, the null hypothesis is rejected.
There is enough evidence to support the claim that the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differs from 64% .
d) No, as its brand is below the average when it comes to approval of the consumers.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differs from 64% .
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.64\\\\H_a:\pi\neq 0.64[/tex]
The significance level is 0.05.
The sample has a size n=100.
The sample proportion is p=0.52.
[tex]p=X/n=52/100=0.52[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.64*0.36}{100}}\\\\\\ \sigma_p=\sqrt{0.0023}=0.048[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.52-0.64+0.5/100}{0.048}=\dfrac{-0.115}{0.048}=-2.3958[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]P-value=2\cdot P(z<-2.3958)=0.0166[/tex]
As the P-value (0.0166) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the percentage of supermarket shoppers who believe that the supermarket ketchup was as good as the national brand ketchup differs from 64% .