For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 502 judges, it was found that 283 were introverts. (a) Let p represent the proportion of all judges who are introverts. Find a point estimate for p. (Round your answer to four decimal places.)

Answer: The largest number was 42

Answer:

80

Step-by-step explanation:

So if 50 tablets are made and 2 are defective then it’s 50:2. That means for every 50 tablets are made 2 are defective. And since 50 goes into 2000 40 times, you would multiply 40 x 2 to get 80, the number defective tablets

Answer:

Step-by-step explanation:

Answer:

We have sufficient evidence to support the claim that the average for the students at Jenna's large high school is greater than 94 minutes.

Step-by-step explanation:

Jenna claims that the average time of texting at her larger high school is greater than 94 minutes per day.

From here we can see that we have to perform a hypothesis test about a sample mean. The null and alternate hypothesis will be:

Null Hypothesis: [tex]\mu \leq 94[/tex]

Alternate Hypothesis: [tex]\mu > 94[/tex]

Jenna collected data from a sample of 32 students. So, sample size will be:

Sample Size = n = 32

Sample Mean = x = 96.5

Sample Standard Deviation = s = 6.3

We have to perform a hypothesis test, to test Jenna's claim. Since, the value of Population Standard Deviation is unknown and the value of Sample Standard Deviation is known, we will use One Sample t-test in this case.

The formula to calculate the test statistic is:

[tex]t=\frac{x-\mu}{\frac{s}{\sqrt{n}}}[/tex]

Using the values, we get:

[tex]t=\frac{96.5-94}{\frac{6.3}{\sqrt{32} } }=2.245[/tex]

The degrees of freedom will be:

df = n - 1 = 32 - 1 = 31

We have to convert the t-score 2.245 with 31 degrees of freedom to its equivalent p-value. From t-table this value comes out to be:

p-value = 0.0160

The significance level is:

[tex]\alpha =0.05[/tex]

Since, the p-value is lesser than the level of significance, we reject the Null Hypothesis.

Conclusion:

We have sufficient evidence to support the claim that the average for the students at Jenna's large high school is greater than 94 minutes.

This p value the significant level  0.05 is given which is higher then the obtained p value. Thus we can reject the null hypothesis. Thus we have convincing statistical evidence to support Jenna’s claim.

Given-

Jenna claims that the average for the students at her large high school is greater than 94 minutes. The null hypothesis is  [tex]\mu\leq 94[/tex]  and alternate hypothesis  [tex]\mu >94[/tex].

Now given that,

The value of sample size [tex]n[/tex] is 32, sample means [tex]x[/tex] is 96.5 and the sample standard deviation [tex]s[/tex] is 6.3.

Here one-sample t-test will be used for the as sample standard deviation is given. The formula for the test statics is,

[tex]t=\dfrac{x-\mu}{\dfrac{s}{\sqrt{n}} }[/tex]

[tex]t=\dfrac{96.5-94}{\dfrac{6.3}{\sqrt{32}} }[/tex]

[tex]t=2.245[/tex]

Now the degrees of freedom is n-1. thus,

[tex]D_f=n-1[/tex]

[tex]D_f=32-1=31[/tex]

Now from the t table the value of t score 2.245 having degree 31 is,

p value[tex]=0.0160[/tex]

For this p value the significant level  0.05 is given which is higher then the obtained p value. Thus we can reject the null hypothesis. Thus we have convincing statistical evidence to support Jenna’s claim.

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Answer:

Yes, there are only 676 different possibilities, which is less than the number of people in the group.

Step-by-step explanation:

Assuming that the English alphabet has 26 different letters, the number of possible combinations of first and last name initials is:

[tex]n = 26*26\\n=676[/tex]

If we try to assign a different combination to each person in the group, it would only be possible to do it for the first 676 people, while the remaining 24 would have a repeated first and last initial. Therefore, the answer is yes, there must be 2 people who have matching first and last initials.

The Pigeonhole Principle in mathematics implies in a group of 700 people, there must be at least two people who have matching first and last initials.

The concept of this problem involves understanding the Pigeonhole Principle in mathematics. Considering the English alphabet has 26 letters, we can have 26 possible first initials and 26 possible last initials. Therefore, there are 26x26=676 unique combinations of first and last initials. However, we have a group of 700 people which is more than 676. The Pigeonhole Principle states that if you try to distribute more items than there are containers, then at least one container must hold more than one item. Therefore, applying this principle, there must be at least two people among the group of 700 who have matching first and last initials because the number of people (700) is greater than the possible unique combinations of first and last initials (676).

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Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $9

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $9

Step-by-step explanation:

We are given that a report on a certain fast food restaurant states that μ, the mean order total, is $9. The manager of the restaurant believes the mean is higher.

A random sample of orders will be selected. The sample mean x¯ will be calculated and used in a hypothesis test to investigate the belief.

Let [tex]\mu[/tex] = the mean order total

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $9

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $9

Here, null hypothesis states that  the mean order total is equal to $9 and the manager claim's is not correct.

On the other hand, alternate hypothesis states that  the mean order total is higher than $9 and the manager claim's is correct.

So, this would be the correct set of hypotheses for testing.

Based on the null hypothesis, the mean order to total is $9, and the manager's belief is wrong. Based on alternate hypothesis, the mean order total is more than $9, and the manager is right.

Given information:

A report on a certain fast food restaurant states that μ, the mean order total, is $9.

The manager of the restaurant believes the mean is higher.

So, according to the null hypothesis, [tex]H_0[/tex]

[tex]\mu=9[/tex]

And, according to alternate hypothesis, [tex]H_a[/tex]

[tex]\mu>9[/tex]

Therefore, based on the null hypothesis, the mean order to total is $9, and the manager's belief is wrong. Based on alternate hypothesis, the mean order total is more than $9, and the manager is right.

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Answer: For every 12 blue pens, she has 6 red pens 12:6

Simplifying this would be: 2:1

Answer:

3 : 1

Step-by-step explanation:

18 : 6

simplified ratio is

3 : 1

Answer: The copy machine makes 171 copies in 4 minutes and 45 seconds.

Step-by-step explanation:

Let's dissect the question. The copy machine makes 36 copies per minute.

36 per min.

To see how many copies it makes in 4 minutes and 45 seconds, we multiply 36 * 4.75. 45 seconds is 3/4ths of a minute, or 0.75 of a minute.

[tex]36 * 4.75=171[/tex]

It makes 171 copies in 4 minutes and 45 seconds.

Answer:

40 and 1/2

Step-by-step explanation:

Multiply 4 1/2 by 1 1/2. Then multiply the product of 4 1/2 and 1 1/2 by 6.

Answer:

b) False

Calculated value Z  =  1.635 < 1.96 at 0.05 level of significance.

The null hypothesis is accepted.

Step-by-step explanation:

Explanation:-

Step:- (1)

Given data the opinion poll recently sampled 1500 voting age citizens.

Given sample size 'n' = 1500

Given data the opinion poll recently sampled 1500 voting age citizens in selected 1020 of the sampled citizens were in favor of an increase in cigarette taxes.

The sample proportion[tex]'p' = \frac{1020}{1500} = 0.68[/tex]

Given data the state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66

Population proportion 'P' =0.66

                                      Q  = 1-P

                                      Q = 1-0.66 = 0.34

Null hypothesis :H₀: 'P' >0.66

Alternative hypothesis: H₀: 'P' <0.66

Level of significance ∝=0.05

Step:-(2)

The test statistic

                             [tex]Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }[/tex]

                            [tex]Z = \frac{0.68-0.66}{\sqrt{\frac{0.66 X 0.34}{1500} } }[/tex]

                            Z  =  1.635

The calculated value   Z  =  1.635

The tabulated value Z = 1.96 at ∝=0.05 level of significance.

Therefore  Z  =  1.635 < 1.96 at 0.05 level of significance.

The null hypothesis is accepted.

The alternative hypothesis is rejected.

Conclusion:-

The null hypothesis is accepted at 0.05 level of significance.

The proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66

Final answer:

The interest earned on $9.02 at an 8% interest rate for three years is $2.16.

Explanation:

To calculate the amount of interest earned on a principal of $9.02 at an interest rate of 8% for three years, we would use the formula for simple interest: Interest = Principal  imes Rate  imes Time. Plugging in the values we get:

Interest = $9.02  imes 0.08  imes 3

Interest = $2.166. Therefore, the interest earned on the principal amount of $9.02 invested at an 8% interest rate for three years would be $2.16, after rounding to the nearest cent.

Vowels are defined as sound repeated as a, e, i, o, u and the rest 21 letters are classified as consonants.

The given words are generated from English alphabet as a combination of Vowels and alphabets. Thus the combination of vowels and consonant help in the formation of words. There are n number of unique letters are formed.

1) Speed is fast = SPEEFAS

2) Minimum number of participants = MINIPART

3) Sum of excess = SUMCESS

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To find the number of unique words that can be generated with a given word length and maximum number of consecutive vowels, multiply the number of possible vowel arrangements by the number of possible consonant arrangements.

To determine the number of unique words that can be generated given the length of a word (wordLen) and the maximum number of consecutive vowels (maxVowels), we need to consider the different possibilities for the arrangement of vowels and consonants in the word. Since vowels can be repeated consecutively up to maxVowels times, we can have up to maxVowels + 1 vowels in a row in any word. Similarly, we can have up to wordLen - maxVowels + 1 consonants in a row in any word. Therefore, the total number of unique words that can be generated is (maxVowels + 1) * (wordLen - maxVowels + 1).

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Answer:

Binomial probability distribution.

Step-by-step explanation:

For each watch, there are only two possible outcomes. Either it fails within 1 year of purchase, or it does not. The probability of a watch falling within 1 year of purchase is independent of other watches. So the type of of distribution will best model the number of watches out of the 15 sampled that fail within 1 year is the binomial probability distribution.

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.

Answer:

The standard deviation of the number of runs required is 2447.26

Step-by-step explanation:

For each run, there are only two possible outcomes. Either the program fails, or it does not. The probability of the computer failing during a run is independent of other runs. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

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

The standard deviation for the expected number of trials for r sucesses is:

[tex]\sqrt{V(X)} = \sqrt{\frac{r(1-p)}{p^{2}}}[/tex]

A computer program has a bug that causes it to fail once in every thousand runs, on average.

This means that [tex]p = \frac{1}{1000} = 0.001[/tex]

In an effort to find the bug, independent runs of the program will be made until the program has failed six times. What is the standard deviation of the number of runs required?

This means that r = 6. So

[tex]\sqrt{V(X)} = \sqrt{\frac{6*0.999}{(0.001)^{2}}} = 2447.26[/tex]

The standard deviation of the number of runs required is 2447.26

Answer:

[tex]t=\frac{255.8-270.74}{\sqrt{\frac{(8.215)^2}{6}+\frac{(11.903)^2}{8}}}}=-2.788[/tex]  

[tex]p_v =2*P(t_{(12)}<-2.788)=0.0164[/tex]

So the p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that we have significant difference in the means of the two groups

Step-by-step explanation:

Data given and notation

Disk:[269.0 249.3 255.2 252.7 247.0 261.6]

Oval:[ 268.8 260.0 273.5 253.9 278.5 289.4 261.6 280.2]

[tex]\bar X_{D}=255.8[/tex] represent the mean for the sample Disk

[tex]\bar X_{O}=270.74[/tex] represent the mean for the sample Oval

[tex]s_{D}=8.215[/tex] represent the sample standard deviation for the sample Disk

[tex]s_{O}=11.903[/tex] represent the sample standard deviation for the sample Oval

[tex]n_{D}=6[/tex] sample size for the group Disk

[tex]n_{O}=8[/tex] sample size for the group Oval

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the means are different, the system of hypothesis would be:

Null hypothesis:[tex]\mu_{D} = \mu_{O}[/tex]

Alternative hypothesis:[tex]\mu_{D} \neq \mu_{O}[/tex]

If we analyze the size for the samples both are less than 30 and the population deviations are not given, so for this case is better apply a t test to compare means, and the statistic is given by:

[tex]t=\frac{\bar X_{D}-\bar X_{O}}{\sqrt{\frac{s^2_{D}}{n_{D}}+\frac{s^2_{O}}{n_{O}}}}[/tex] (1)

t-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

Calculate the statistic

We can replace in formula (1) the results obtained like this:

[tex]t=\frac{255.8-270.74}{\sqrt{\frac{(8.215)^2}{6}+\frac{(11.903)^2}{8}}}}=-2.788[/tex]  

Statistical decision

For this case we don't have a significance level provided [tex]\alpha[/tex], but we can calculate the p value for this test. The first step is calculate the degrees of freedom, on this case:

[tex]df=n_{D}+n_{O}-2=6+8-2=12[/tex]

Since is a bilateral test the p value would be:

[tex]p_v =2*P(t_{(12)}<-2.788)=0.0164[/tex]

So the p value is a very low value and using any significance level for example [tex]\alpha=0.05, 0,1,0.15[/tex] always [tex]p_v<\alpha[/tex] so we can conclude that we have enough evidence to reject the null hypothesis, and there is enough evidence to conclude that we have significant difference in the means of the two groups

Answer: b

Step-by-step explanation:

The solutions to the quadratic equation x^2 = -5x - 3 are (-5 - sqrt(13))/2 and (-5 + sqrt(13))/2, calculated using the quadratic formula -b ± √(b² - 4ac) / (2a).

The subject of this question is Mathematics, specifically, the solution of quadratic equations. A quadratic equation is in the form ax²+bx+c = 0. You can find the solutions or roots of any quadratic equation using the formula: -b ± √(b² - 4ac) / (2a).

Let's apply this formula to the quadratic equation, x^2 = -5x - 3. Here, a = 1, b = 5, and c = 3. Substituting these values into the formula, the solutions to this quadratic equation are (-5 - sqrt(13))/2 and (-5 + sqrt(13))/2. However, in the question, there seems to be multiple options. It's essential to note that the correct solutions match the ones derived from our calculations.

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Answer:

x = 5/3

y = 14/3

Step-by-step explanation:

y=4x−2

y=x+3

​Since they are both equal to y, we can set them equal to each other

4x-2 = x+3

Subtract x from each side

4x-2-x = x+3-x

3x-2 =3

Add 2 to each side

3x-2+2 = 3+2

3x =5

Divide each side by 3

3x/3 =5/3

x = 5/3

Now we need to find y

y = x+3

y =5/3+3

y = 5/3+9/3

y = 14/3

Answer:

x=5/3; y=14/3

Step-by-step explanation:

Subtract the following:

-4x+y=-2

-x+y=3

= -3x=-5

x=5/3

substitute x into one of the given equations.

y=5/3+3

y= 14/3

Answer:

2 seconds and 38 seconds

Step-by-step explanation:

h=-16t²-vot

1,200=-16t²-640t

turn this into standard form

16t²-640t+1200=0

now plug thes numbers into the quadratice formula

a 16 b -640 c 1200

solve with quadratic formula to get ≅2 and ≅38 seconds

Answer:

t≈2 seconds,t≈38 seconds

Step-by-step explanation:

h=−16t2+ v0t

Step 1. Solve the equation.

1,200= −16t^2+ 640t

We know the velocity, v0, is 640 feet per second.

The height is 1,200 feet. Substitute the values.

This is a quadratic equation. Rewrite it in standard form. Solve the equation using the quadratic formula.

ax^2 +   bx  +      c .   = 0

16t^2 −640t +  1,200 = 0

Identify the values of a, b, and c.

a=16,  b=−640, c=1,200

Write the quadratic formula.

t=−b± √b2−4ac‾‾‾‾‾‾‾‾

               2a

640+ √332,800‾‾‾‾‾‾‾‾   t= √640− √332,800‾‾‾‾‾‾‾

             32                                           32

Rewrite to show two solutions.

t=640+332,800‾‾‾‾‾‾‾‾√32,t=640−332,800‾‾‾‾‾‾‾‾√32

Approximate the answer with a calculator.

t≈2 seconds,t≈38 seconds

Step 2. Check the answer. The check is left to you.

Step 3. Answer the question.

The firework will go up and then fall back down. As the firework goes up, it will reach 1,200 feet after approximately 2 seconds. It will also pass that height on the way down at 38 seconds.

Answer:

18.15% probability of producing a bad product

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

[tex]\mu = 3.01, \sigma = 0.02[/tex]

What is the probability of producing a bad product?

Less than 2.97 or more than 3.03.

Less than 2.97

pvalue of Z when X = 2.97. So

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

[tex]Z = \frac{2.97 - 3.01}{0.02}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a pvalue of 0.0228

More than 3.03

1 subtracted by the pvalue of Z when X = 3.03. So

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

[tex]Z = \frac{3.03 - 3.01}{0.02}[/tex]

[tex]Z = 1[/tex]

[tex]Z = 1[/tex] has a pvalue of 0.8413

1 - 0.8413 = 0.1587

Then

0.0228 + 0.1587 = 0.1815

18.15% probability of producing a bad product

Answer:

8 1/3

Step-by-step explanation:

2 1/2 * 3 1/3

Change each to an improper fraction

2 1/2  = (2*2 +1)/2 = 5/2

3 1/3 = (3*3+1)/3 = 10/3

5/2 *10/3 = 50/6

Divide the top and bottom by 2

25/3

Change to a mixed number

3 goes into 25    8 times with 1 left over

8 1/3

Answer:

0.233

Step-by-step explanation:

There are a total of 16 marbles.

The probability the first marble is blue is 8/16.

Assuming the marble isn't replaced, the probability the second marble is blue is 7/15.

So the probability of both marbles being blue is 8/16 × 7/15 = 7/30 ≈ 0.233.

The probability of drawing two blue marbles without replacement is 0.233 to the nearest thousandth, calculated by multiplying the individual probabilities of the first and second draws.

The probability of drawing two blue marbles from a bag without replacement involves a two-step calculation because the outcome of the first draw affects the second. Since there are 3 red, 8 blue, and 5 green marbles, the total number of marbles is 16. The probability of drawing a blue marble first is 8/16 or 1/2.

After drawing one blue marble, there would be 7 blue marbles left in a bag of 15 total marbles. The probability of drawing a blue marble on the second draw is then 7/15. To find the combined probability of both events occurring, we multiply the two probabilities: (1/2) × (7/15) = 7/30, which is approximately 0.233 to the nearest thousandth.

Thus, the probability of drawing two blue marbles in a row without replacement is 0.233 to the nearest thousandth.

Answer:

32¾

Step-by-step explanation:

1 pound (lb) = 16 ounces

12 oz = 12/16 = 3/4 lb

32 pounds 12 oz

32 ¾ lb

Answer:

Expected number of matches that occur = 4 matches

Step-by-step explanation:

First of all, let X_i be the event that when we turn over card i if it matches the required cards face.

Thus, for example X_1 is the event that turning over one card results in an ace while X_2 is the event that turning over second card reveals a deuce.

The number of matched cards "N" is given by the sum of this indicator random variable as shown in the attached file;

The expected number of matches when cards are drawn from a standard 52-card deck is 4.

We define a match for each card position as X_i = 1 if a match occurs, and X_i = 0 otherwise. The expectation E(X_i) for each card is 1/13 because the probability of the ith card being an i-matched card (Ace in the 1st position, Two in the 2nd position, and so on up to King in the 13th, then repeat with Ace) is 1/13.

Given there are 52 cards, each having the same pattern of matching, the expected number of matches is computed as:

E(X) = E(X_1 + X_2 + ... + X_52) = E(X_1) + E(X_2) + ... + E(X_52)

Since E(X_i) = 1/13 for all i:

E(X) = 52 * (1/13) = 4

Therefore, the expected number of matches is 4.

Answer:

bcd

Step-by-step explanation:

Answer:

B C D

Step-by-step explanation:

Answer:

A = 81 pi ft^2

Step-by-step explanation:

The area of a circle is found by

A = pi r^2

The radius is 9

A = pi 9^2

A = 81 pi ft^2

Answer:

The maximum price that the dealer will sell is $7471 and the minimum is $5513.

Step-by-step explanation:

Problems of normally distributed samples are 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.

In this problem, we have that:

[tex]\mu = 6492, \sigma = 1025[/tex]

Middle 66%

50 - (66/2)  = 17th percentile

50 + (66/2) = 83rd percentile

17th percentile

X when Z has a pvalue of 0.17. So X when Z = -0.955.

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

[tex]-0.955 = \frac{X - 6492}{1025}[/tex]

[tex]X - 6492 = -0.955*1025[/tex]

[tex]X = 5513[/tex]

83rd percentile

X when Z has a pvalue of 0.83. So X when Z = 0.955.

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

[tex]0.955 = \frac{X - 6492}{1025}[/tex]

[tex]X - 6492 = 0.955*1025[/tex]

[tex]X = 7471[/tex]

The maximum price that the dealer will sell is $7471 and the minimum is $5513.

Answer:

[tex]\chi^2 =\frac{4-1}{0.7^2} 1.5^2 =13.776[/tex]

[tex]p_v =P(\chi^2 >13.776)=0.0032[/tex]

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(13.776,3,TRUE)"

If we compare the p value and the significance level assumed we see that [tex]p_v <\alpha[/tex] so on this case we have enough evidence in order reject the null hypothesis. And we can conclude that the true deviation i significantly higher than 0.7

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

[tex]n=4[/tex] represent the sample size

We can calculate the sample deviation with this formula:

[tex]s = \sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}[/tex]

[tex]\alpha[/tex] represent the confidence level  

[tex]s =1.5 [/tex] represent the sample variance obtained

[tex]\sigma^2 =0.7[/tex] represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population deviation is higher than 0.7, so the system of hypothesis would be:

Null Hypothesis: [tex]\sigma \leq 0.7[/tex]

Alternative hypothesis: [tex]\sigma >0.7[/tex]

Calculate the statistic  

For this test we can use the following statistic:

[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

[tex]\chi^2 =\frac{4-1}{0.7^2} 1.5^2 =13.776[/tex]

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case 3. And since is a right tailed test the p value would be given by:

[tex]p_v =P(\chi^2 >13.776)=0.0032[/tex]

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(13.776,3,TRUE)"

Conclusion

If we compare the p value and the significance level assumed we see that [tex]p_v <\alpha[/tex] so on this case we have enough evidence in order reject the null hypothesis. And we can conclude that the true deviation i significantly higher than 0.7

Answer:

.54444 = .54444/1 = 5.4444/10 = 54.444/100 = 544.44/1000 = 5444.4/10000 = 54444/100000, any one of those works

Answer:

54/99

Step-by-step explanation:

Answer:

large of a sample size  n = 2645

Step-by-step explanation:

Explanation:-

The population standard deviation 'σ' = 39.9

Given data the estimate is within 2 of the true population mean so given the margin of error = 2

we know that margin of error is determined by

Margin of error = [tex]\frac{z_{\alpha }S.D }{\sqrt{n} }[/tex]

cross multiplication , we get

                    [tex]\sqrt{n} = \frac{2.578 X S.D}{M.E}[/tex]

                    [tex]\sqrt{n} = \frac{2.578 X 39.9}{2}= 51.4311[/tex]

squaring on both sides , we get

                    n = 2645.15

                    n = 2645

Conclusion:-

large of a sample size  n = 2645

Answer:

3.8

Step-by-step explanation: