Deck 6: Inferences Based on a Single Sample: Estimation With Confidence Intervals

Question 1

Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sample 468 of its members at random and monitor the working time of each of them for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. Which of the following should be used to estimate the parameter of interest for this problem?

A) A small sample confidence interval for µ.
B) A large sample confidence interval for p.
C) A small sample confidence interval for p.
D) A large sample confidence interval for µ.

Answer 1

A large sample confidence interval for µ.

Question 2

Answer 2

C

Question 3

Suppose you want to estimate a population proportion $p$ where $\hat { p } = 0.61 , n = 1000$ , and $N = 7500$ . Find an approximate $95 \%$ confidence interval for p.

A) $0.61 \pm .046$
B) $0.61 \pm .056$
C) $0.61 \pm .036$
D) $0.61 \pm .029$

Answer 3

$0.61 \pm .029$

Question 4

The registrar's office at State University would like to determine a 95% confidence interval for the mean commute time of its students. A member of the staff randomly chooses a parking lot and surveys the first 125 students who park in the chosen lot on a given day. The confidence interval is

A) not meaningful because of the lack of random sampling.
B) not meaningful because the sampling distribution of the sample mean is not normal.
C) meaningful because the sample is representative of the population.
D) meaningful because the sample size exceeds 30 and the Central Limit Theorem ensures normality of the sampling distribution of the sample mean.

Question 5

It is desired to estimate the proportion of college students who feel a sudden relief now that their statistics class is over. How many students must be sampled in order to estimate the true proportion to within 2% at the 90% confidence level?

A) $n = 189$
B) $n = 2401$
C) $n = 133$
D) $n = 1692$
E) Cannot determine because no estimate of $p$ or $q$ exists in this problem

Question 6

Suppose it is desired to estimate the average time a customer spends in a particular store to withir 5 minutes (e.g., $\pm 5$ minutes) at $99 \%$ reliability. It is estimated that the standard deviation of the times is 15 minutes. How large a sample should be taken to get the desired interval?

A) $n = 35$
B) $n = 25$
C) $\mathrm { n } = 60$
D) $\mathrm { n } = 299$

Question 7

Which statement best describes a parameter?

A) A parameter is an unbiased estimate of a statistic found by experimentation or polling.
B) A parameter is a numerical measure of a population that is almost always unknown and must be estimated.
C) A parameter is a sample size that guarantees the error in estimation is within acceptable limits.
D) A parameter is a level of confidence associated with an interval about a sample mean or proportion.

Question 8

A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of the students responded that they considered themselves full-time students. A computer program was used to generate the following 95% confidence interval for the population proportion: (0.64814,
0.75186). Which of the following practical interpretations is correct for this confidence interval?

A) We are 95% confident that the percentage of the 300 students who responded that they considered themselves full-time students was 0.700.
B) We are 95% confident that the percentage of all college students who consider themselves full-time students falls between 0.648 and 0.752.
C) We are 95% confident that the percentage of all college students who consider themselves full-time students was 0.700.
D) We are 95% confident that the percentage of the 300 students who responded that they considered themselves full-time students falls between 0.648 and 0.752.

Question 9

It is desired to estimate the average time it takes Statistics students to finish a computer project to within two hours at 90% reliability. It is estimated that the standard deviation of the times is 14 hours. How large a sample should be taken to get the desired interval?

A) $n = 189$
B) $n = 231$
C) $\mathrm { n } = 325$
D) $n = 133$

Question 10

A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects
(60-year-old male non-smokers) and constructed the following 95 percent confidence interval for the mean cost of the term life insurance: ($850.00, $1050.00). Explain what the phrase "95 percent confident" means in this situation.

A) 95 percent of all the life insurance costs will fall within the specified interval.
B) In repeated sampling, 95 percent of the intervals constructed would contain the value of the true population mean.
C) 95 percent of all retired statisticians are underinsured.
D) In repeated sampling, the mean of the population will fall within the specified intervals 95 percent of the time.

Question 11

A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects (60-year-old male non-smokers) and constructed the following 95 percent confidence interval for the mean cost of the term life insurance: ($850.00, $1050.00). What value of alpha was used to create this confidence interval?

A) 0.025
B) 0.10
C) 0.05
D) 0.01

Question 12

Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested in estimating the average parking time of students from within the various colleges on campus. A survey of 338 College of Business (COBA) students yields the following descriptive information regarding the length of time (in minutes) it took them to find a parking spot. Note that the "Lo 95%" and "Up 95%" refer to the endpoints of the desired confidence interval.

$\begin{array}{lccccc}\text { Variable } & \mathrm{N} & \text { Lo } 95 \% \text { CI } & \text { Mean } & \text { Up 95\% CI } & \text { SD } \\\text { Parking Time } & 338 & 9.1944 & 10.466 & 11.738 & 11.885\end{array}$

Give a practical interpretation for the 95% confidence interval given above.

A) 95% of the COBA students had parking times that fell between 9.19 and 11.74 minutes.
B) We are 95% confident that the average parking time of the 338 COBA students surveyed falls between 9.19 and 11.74 minutes.
C) 95% of the COBA students had parking times of 10.466 minutes.
D) We are 95% confident that the average parking time of all COBA students falls between 9.19 and 11.74 minutes.

Question 13

A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects (60-year-old male non-smokers) and constructed the following 95 percent confidence interval for
The mean cost of the term life insurance: ($850.00, $1050.00). State the appropriate interpretation for this confidence interval. Note that all answers begin with "We are 95 percent confidence that…"

A) The term life insurance cost of the retired statistician's insurance policy falls between $850.00 and $1050.00
B) The term life insurance cost for all 60-year-old male non-smokers' insurance policies falls between $850.00 and $1050.00
C) The average term life insurance cost for sampled 65 subjects falls between $850.00 and $1050.00
D) The average term life insurance costs for all 60-year-old male non-smokers falls between $850.00 and $1050.00

Question 14

A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of the students responded that they considered themselves full-time students. A computer program was used to generate the following 95% confidence interval for the population proportion: (0.64814,
0.75186). The sample size that was used in this problem is considered a large sample. What criteria should be used to determine if n is large?

A) If $\mathrm { n } > 25$ , then $\mathrm { n }$ is considered large.
B) Both $\hat { n p } \geq 15$ and $\hat { n q } \geq 15$ .
C) When working with proportions, any $\mathrm { n }$ is considered large.
D) If $\mathrm { n } \geq 30$ , then $\mathrm { n }$ is considered large.

Question 15

Question 16

A study was conducted to determine what proportion of all college students considered themselves as full-time students. A random sample of 300 college students was selected and 210 of the students responded that they considered themselves full-time students. Which of the following would represent the target parameter of interest?

A) µ
B) p

Question 17

How much money does the average professional football fan spend on food at a single football game? That question was posed to 60 randomly selected football fans. The sampled results show that the sample mean was $70.00 and prior sampling indicated that the population standard deviation was $17.50. Use this information to create a 95 percent confidence interval for the population mean

A) $70 \pm 1.833 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$

B) $70 \pm 1.645 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$

C) $70 \pm 1.960 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$

D) $70 \pm 1.671 \left( \frac { 17.50 } { \sqrt { 60 } } \right)$

Question 18

Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested in estimating the average parking time of students from within the various colleges on campus. A survey of 338 College of Business (COBA) students yields the following descriptive information regarding the length of time (in minutes) it took them to find a parking spot. Note that the "Lo 95%" and "Up 95%" refer to the endpoints of the desired confidence interval.

$$\begin{array} { l c c c c c } \text { Variable } & \text { N } & \text { Lo 95\% CI } & \text { Mean } & \text { Up 95\% CI } & \text { SD } \\\text { Parking Time } & 338 & 9.1944 & 10.466 & 11.738 & 11.885\end{array}$$
Explain what the phrase "95% confident" means when working with a 95% confidence interval.

A) In repeated sampling, 95% of the sample means will fall within the interval created.
B) In repeated sampling, 95% of the population means will fall within the interval created.
C) In repeated sampling, 95% of the intervals created will contain the population mean.
D) 95% of the observations in the population will fall within the endpoints of the interval.

Question 19

Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested in estimating the average parking time of students from within the various colleges on campus. A survey of 338 College of Business (COBA) students yields the following descriptive information regarding the length of time (in minutes) it took them to find a parking spot. Note that the "Lo 95%" and "Up 95%" refer to the endpoints of the desired confidence interval.

$$\begin{array} { l l c r c r r } \text { Variable } & \mathrm { N } & \text { Lo 95\% CI } & \text { Mean } & \text { Up 95\% CI } & \text { SD } \\\text { Parking Time } & 338 & 9.1944 & 10.466 & 11.738 & 11.885\end{array}$$
University officials have determined that the confidence interval would be more useful if the interval were narrower. Which of the following changes in the confidence level would result in a narrower interval?

A) The university could increase their confidence level.
B) The university could decrease their confidence level.

Question 20

The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 49 different 24-hour periods and determines the number of admissions for each. For this sample, $\bar { x } = 17.2$ and $s ^ { 2 } = 25$ . Estimate the mean number of admissions per 24 -hour period with a $90 \%$ confidence interval.

A) $17.2 \pm .643$
B) $17.2 \pm .168$
C) $17.2 \pm 5.875$
D) $17.2 \pm 1.175$

Question 21

Calculate the percentage of the population sampled if n = 250 and N = 1000. Should the standard error in this situation be multiplied by a finite population correction factor?
Explain.

Question 22

Question 23

For $n = 40 \text { and } \hat { p } = .35 \text {, is }$ s the sample size large enough to construct a confidence for p?

Question 24

A newspaper reports on the topics that teenagers most want to discuss with their parents. the findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 505 teenagers. Estimate the proportion of all teenagers who want more family discussions about religion. Use a 90% confidence level.

Question 25

A random sample of 80 observations produced a mean $\bar { x } = 35.4$ and a standard deviation $= 3.1$ .
a. Find a $90 \%$ confidence interval for the population mean $\mu$ .
b. Find a $95 \%$ confidence interval for $\mu$ .
c. Find a $99 \%$ confidence interval for $\mu$ .
d. What happens to the width of a confidence interval as the value of the confidence coefficient is increased while the sample size is held fixed?

Question 26

A random sample of 50 employees of a large company was asked the question, "Do you participate in the company's stock purchase plan?" The answers are shown below.

$$\begin{array} { l l l l l l l l l l } \text { yes } & \text { no } & \text { no } & \text { yes } & \text { no } & \text { no } & \text { yes } & \text { yes } & \text { no } & \text { no } \\\text { no } & \text { yes } & \text { yes } & \text { yes } & \text { no } & \text { yes } & \text { no } & \text { no } & \text { yes } & \text { yes } \\\text { no } & \text { yes } & \text { yes } & \text { no } & \text { yes } & \text { yes } & \text { no } & \text { yes } & \text { yes } & \text { yes } \\\text { yes } & \text { no } & \text { no } & \text { yes } & \text { yes } & \text { yes } & \text { yes } & \text { yes } & \text { no } & \text { yes } \\\text { no } & \text { yes } & \text { yes } & \text { no } & \text { yes } & \text { yes } & \text { yes } & \text { yes } & \text { yes } & \text { yes }\end{array}$$ Use a 90% confidence interval to estimate the proportion of employees who participate in the company's stock purchase plan.

Question 27

Question 28

Question 29

The following sample of 16 measurements was selected from a population that is approximately normally distributed.

$\begin{array} { l l l l l l l l } 61 & 85 & 92 & 77 & 83 & 81 & 75 & 78 \end{array}$
$\begin{array} { l l l l l l l l } 95 & 87 & 69 & 74 & 76 & 84 & 80 & 83 \end{array}$

Construct a 90% confidence interval for the population mean.

Question 30

A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 90% confidence interval was calculated to be ($2,181,260, $5,836,180). Give a practical interpretation of the confidence interval.

Question 31

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood.

$\begin{array}{rl}X=&\text { saleprice }\\\\\text {SAMPLE MEAN OF X} =&46300 \\\text {SAMPLE STANDARD DEV } =&13747 \\ \text {SAMPLE SIZE OF X} =&25 \\\text {CONEIDENCE}=& 90 \\\\\text { UPPER LIMIT }= & 51003.90 \\\text { SAMPLE MEAN OF X }= & 46300 \\\text { LOWER LIMIT }= & 41596.10\end{array}$

A friend suggests that the mean sale price of homes in this neighborhood is $47,000. Comment on your friend's suggestion.

Question 32

A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Based on the interval above, do you believe the average total compensation of CEOs in the service industry is more than $1,500,000?

Question 33

Parking at a large university can be extremely difficult at times. One particular university is trying to determine the location of a new parking garage. As part of their research, officials are interested in estimating the average parking time of students from within the various colleges on campus.
Which of the following would represent the target parameter of interest?

A) $\mu$
B) $p$

Question 34

Suppose that 100 samples of size $n = 50$ are independently chosen from the same population and that each sample is used to construct its own $95 \%$ confidence interval for an unknown population mean $\mu$ . How many of the 100 confidence intervals would you expect to actually contain $\mu$ ?

Question 35

What is the rule of thumb for the finite population correction factor?

Question 36

Suppose you wanted to estimate a binomial proportion, p, correct to within .03 with probability 0.90. What size sample would need to be selected if p is known to be approximately 0.7?

Question 37

The following data represent the scores of a sample of 50 randomly chosen students on a standardized test.

$$\begin{array} { l l l l l l l l l l } 39 & 48 & 55 & 63 & 66 & 68 & 68 & 69 & 70 & 71 \\71 & 71 & 73 & 74 & 76 & 76 & 76 & 77 & 78 & 79 \\79 & 79 & 79 & 80 & 80 & 82 & 83 & 83 & 83 & 85 \\85 & 86 & 86 & 88 & 88 & 88 & 88 & 89 & 89 & 89 \\90 & 91 & 92 & 92 & 93 & 95 & 96 & 97 & 97 & 99\end{array}$$ a. Write a 95% confidence interval for the mean score of all students who took the test.
b. Identify the target parameter and the point estimator.

Question 38

A random sample of $n = 144$ measurements was selected from a population with unknown mean $\mu$ and standard deviation $\sigma$ . Calculate a $90 \%$ confidence interval if $\bar { x } = 3.55$ and $s =$ .49

Question 39

A local men's clothing store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will choose a random sample from the 100,000 items in the store's inventory in order to determine the proportion of merchandise that is outdated. The current owners have never determined the percentage of outdated merchandise and cannot help the buyers. How large a sample do the buyers need in order to be 95% confident that the margin of error of their estimate is within 3%?

Question 40

When is the finite population correction factor used?

Question 41

A random sample of 4000 U.S. citizens yielded 2280 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation.

A) .4300
B) 2280
C) .5700
D) 4000

Question 42

Let t0 be a particular value of t. Find a value of

Question 43

You are interested in purchasing a new car. One of the many points you wish to consider is the resale value of the car after 5 years. Since you are particularly interested in a certain foreign sedan, you decide to estimate the resale value of this car with a 95% confidence interval. You manage to obtain data on 17 recently resold 5-year-old foreign sedans of the same model. These 17 cars were resold at an average price of $13,200 with a standard deviation of $700. Create a 95% confidence interval for the true mean resale value of a
5-year-old car of that model.

Question 44

$$\text { For } n = 800 \text { and } \hat { p } = .99 \text {, is the sample size large enough to construct a confidence for } p \text { ? }$$

Question 45

Question 46

A random sample of 250 students at a university finds that these students take a mean of 15.3 credit hours per quarter with a standard deviation of 1.6 credit hours. Estimate the mean credit hours taken by a student each quarter using a 95% confidence interval. Round to the nearest thousandth.

A) $15.3 \pm .198$
B) $15.3 \pm .010$
C) $15.3 \pm .013$
D) $15.3 \pm .157$

Question 47

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 1% with 90% reliability, how many
Students would need to be sampled?

A) 66
B) 1584
C) 3980
D) 6546

Question 48

Suppose you selected a random sample of n = 7 measurements from a normal distribution.
Compare the standard normal z value with the corresponding t value for a 90% confidence interval.

Question 49

For $n = 40 \text { and }\hat { p} = .45 \text {, }$ s the sample size large enough to construct a confidence for p?

Question 50

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). Which of the following statements is true?

A) In construction of the confidence interval, a z-value was used.
B) In construction of the confidence interval, a z-value with 20 degrees of freedom was used.
C) In construction of the confidence interval, a t-value with 19 degrees of freedom was used.
D) In construction of the confidence interval, a t-value with 20 degrees of freedom was used.

Question 51

A marketing research company is estimating the average total compensation of CEOs in the service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180). What additional assumption is necessary for this confidence interval to be valid?

A) The sample standard deviation is less than the degrees of freedom.
B) None. The Central Limit Theorem applies.
C) The population of total compensations of CEOs in the service industry is approximately normally distributed.
D) The distribution of the sample means is approximately normal.

Question 52

The following random sample was selected from a normal population: 9, 11, 8, 10, 14, 8. Construct a 95% confidence interval for the population mean

Question 53

The U.S. Commission on Crime randomly selects 600 files of recently committed crimes in an area and finds 380 in which a firearm was reportedly used. Find a 99% confidence interval for p, the true fraction of crimes in the area in which some type of firearm was reportedly used.

Question 54

How much money does the average professional football fan spend on food at a single football game? That question was posed to 43 randomly selected football fans. The sample results provided a sample mean and standard deviation of $16.00 and $2.85, respectively.
Find and interpret a 99% confidence interval for $\mu .$

Question 55

Suppose (1,000, 2,100) is a 95% confidence interval for µ. To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Explain why an increase in sample size will lead to a narrower interval of the estimate of $\mu _ { c }$

Question 56

Calculate the percentage of the population sampled if n = 100 and N = 10,000. Should the standard error in this situation be multiplied by a finite population correction factor?
Explain.

Question 57

The standard deviation of a population is estimated to be 295 units. To estimate the population mean to within 46 units with 95% reliability, what size sample should be selected?

Question 58

Sales of a new line of athletic footwear are crucial to the success of a newly formed company. The company wishes to estimate the average weekly sales of the new footwear to within $150 with 90% reliability. The initial sales indicate that the standard deviation of the weekly sales figures is approximately $1500. How many weeks of data must be sampled for the company to get the information it desires?

Question 59

The daily intakes of milk (in ounces) for ten five-year old children selected at random from one school were: $$\begin{array} { l l l l l } 21.7 & 27.9 & 12.2 & 25.7 & 16.9 \\17.7 & 12.2 & 31.1 & 14.0 & 28.0\end{array}$$

Find a 99% confidence interval for the standard deviation, ?, of the daily milk intakes of all five-year olds at this school. Round to the nearest hundredth when necessary.

A) (0.95, 3.51)
B) (4.24, 14.50)
C) (4.38, 14.50)
D) (4.38, 16.14)

Question 60

What is

A) 2.575
B) 2.33
C) 1.645
D) 1.96

Question 61

A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 95% confidence interval for the proportion of college students who prefer drink A: (.453, .493). Identify the point estimate for estimating the true proportion of college students who prefer that drink.

A) .493
B) .453
C) .02
D) .473

Question 62

What is the confidence level of the following confidence interval for $\mu$ ?
$\bar { x } \pm 2.33 \left( \frac { \sigma } { \sqrt { n } } \right)$

A) 233%
B) 67%
C) 78%
D) 98%

Question 63

One way of reducing the width of a confidence interval is to reduce the size of the sample taken.

Question 64

A random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval.

A) $.5625 \pm .0129$
B) $.5625 \pm .4048$
C) $.4375 \pm .4048$
D) $.4375 \pm .0129$

Question 65

Calculate the finite population correction factor for $\mathrm { n } = 300 \text { and } \mathrm { N } = 1500$

A) .4472
B) .8000
C) 2.000
D) .8944

Question 66

For data with two outcomes (success or failure), the binomial proportion of successes is likely to be the parameter of interest.

Question 67

A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.2%). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?

A) 1.05%
B) 2.1%
C) 2.15%
D) 1.60%

Question 68

Question 69

Let $t _ { 0 }$ be a specific value of $t$ . Find $t _ { 0 }$ such that the following statement is true: $P \left( t \geq t _ { 0 } \right) = .05$ where $\mathrm { df } = 20$ .

A) -1.729
B) $1.729$
C) $- 1.725$
D) $1.725$

Question 70

A) 97%
B) 3%
C) 98.5%
D) 94%

Question 71

What is the confidence coefficient in a 95% confidence interval for $\mu$ ?

A) .95
B) .025
C) .05
D) .475

Question 72

Given the values of $\bar { x } , \mathrm {~s}$ , and n, form a $99 \%$ confidence interval for $\sigma$ .
$\bar { x } = 17.3 , s = 7.5 , n = 24$

A) (29.28, 139.71)
B) (5.41, 11.82)
C) (5.57, 11.26)
D) (3.9, 18.63)

Question 73

What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. A computer package was used to generate the printout below of a 90% confidence intervaln for the proportion of college students who prefer American automobiles.

SAMPLE PROPORTION $= .396$
$\text { SAMPLE SIZE = } 159$

UPPER LIMIT $= .460$
LOWER LIMIT $= .332$

Based on the interval above, do you believe that 31% of all college students prefer American automobiles?

A) No, and we are 100% sure of it.
B) No, and we are 90% confident of it.
C) Yes, and we are 90% confident of it.
D) Yes, and we are 100 %sure of it.

Question 74

Since the population standard deviation ? is almost always known, we use it instead of the sample standard deviation s when finding a confidence interval.

Question 75

If no estimate of p exists when determining the sample size for a confidence interval for a proportion, we can use .5 in the formula to get a value for n.

Question 76

The sampling distribution for $\hat{p}$ is approximately normal for a large sample size $n$ , where $n$ is considered large if both $n \hat { p } \geq 15$ and $n ( 1 - \hat { p } ) \geq 15$ .

Question 77

A random sample of 15 crates have a mean weight of 165.2 pounds and a standard deviation of 15.3 pounds. Construct a 95% confidence interval for the population standard deviation ?. Assume the population is normally distributed, and round to the nearest hundredth when necessary.

A) (2.86, 6.17)
B) (125.47, 582.24)
C) (11.76, 22.33)
D) (11.2, 24.13)

Question 78

A sociologist develops a test to measure attitudes towards public transportation, and 47 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4.
Construct an approximate 95% confidence interval for the mean score of all such subjects.

A) $76.2 \pm 0.91$
B) $76.2 \pm 6.87$
C) $76.2 \pm 6.24$
D) $76.2 \pm 3.12$

Question 79

Question 80

A previous random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. How many citizens would need to be sampled for a 95% confidence interval to estimate the true proportion within 2%?

A) 2364
B) 2498
C) 2209
D) 2401