Deck 7: Inferences Based on a Single Sample: Estimation With Confidence Intervals

Question 1

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) p
B) μ

Answer 1

A

Question 2

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

Answer 2

The university could decrease their confidence level.

Question 3

Explain what the phrase 95% confident means when we interpret a 95% confidence interval for μ.

A) In repeated sampling, 95% of similarly constructed intervals contain the value of the population mean.
B) 95% of similarly constructed intervals would contain the value of the sampled mean.
C) 95% of the observations in the population fall within the bounds of the calculated interval.
D) The probability that the sample mean falls in the calculated interval is 0.95.

Answer 3

A

Question 4

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) 0.10
B) 0.05
C) 0.025
D) 0.01

Question 5

Which statement best describes a parameter?

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

Question 6

For quantitative data, the target parameter is most likely to be the mode of the data.

Question 7

The confidence coefficient is the relative frequency with which the interval estimator encloses the population parameter when the estimator is used repeatedly a very large number of times.

Question 8

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($130,852, $147,990). To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?

A) Increase the sample size and decrease the confidence level.
B) Decrease the sample size and decrease the confidence level.
C) Increase the sample size and increase the confidence level.
D) Decrease the sample size and increase the confidence level.

Question 9

What is $z \alpha / 2 \text { when } \alpha = 0.05$ ?

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

Question 10

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

Question 11

One way of reducing the width of a confidence interval is to reduce the confidence level.

Question 12

The confidence level is the confidence coefficient expressed as a percentage.

Question 13

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) p
B) μ

Question 14

The Central Limit Theorem guarantees an approximately normal sampling distribution for the sample mean for large sample sizes, so no knowledge about the distribution of the population is necessary for the corresponding interval to be valid.

Question 15

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

Question 16

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

Question 17

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 μ.

Question 18

A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.3%, 5%). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?

A) 3.15%
B) 1.85%
C) 2.50%
D) 3.7%

Question 19

What is the confidence level of the following confidence interval for ?? $\bar { x } \pm 1.96 \left( \frac { \sigma } { \sqrt { n } } \right)$

A) 95%
B) 98%
C) 99%
D) 196%

Question 20

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

Question 21

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) In repeated sampling, the mean of the population will fall within the specified intervals 95 percent of the time.
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) 95 percent of all the life insurance costs will fall within the specified interval.

Question 22

A random sample of 250 students at a university finds that these students take a mean of 15.6 credit hours per quarter with a standard deviation of 2.2 credit hours. Estimate the mean credit hours taken by a student each quarter using a 98% confidence interval. Round to the nearest thousandth.

Question 23

The following data represent the scores of a sample of 50 randomly chosen students on a standardized test. 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 24

A random sample of 250 students at a university finds that these students take a mean of 15.4 credit hours per quarter with a standard deviation of 2.2 credit hours. The 99% confidence interval for the mean is 15.4 ± 0.358. Interpret the interval.

A) We are 99% confident that the average number of credit hours per quarter of students at the university falls in the interval 15.042 to 15.758 hours.
B) 99% of the students take between 15.042 to 15.758 credit hours per quarter.
C) We are 99% confident that the average number of credit hours per quarter of the sampled students falls in the interval 15.042 to 15.758 hours.
D) The probability that a student takes 15.042 to 15.758 credit hours in a quarter is 0.99.

Question 25

Determine the confidence level for the given confidence interval for ?. $\bar { x } \pm 1.48 \left( \frac { \sigma } { \sqrt { n } } \right)$

A) 86%
B) 93%
C) 7%
D) 96.5%

Question 26

A random sample of n measurements was selected from a population with unknown mean μ and known standard deviation σ. Calculate a 95% confidence interval for μ for the given situation. Round to the nearest hundredth when necessary.

Question 27

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.

A) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.
B) 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144.
C) We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.
D) 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144.

Question 28

Which information is not shown on the screen below?

A) the confidence level
B) the sample mean
C) the sample standard deviation
D) the sample size

Question 29

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 average term life insurance cost for sampled 65 subjects falls between $850.00 and $1050.00
B) The term life insurance cost of the retired statistician's insurance policy falls between $850.00 and $1050.00
C) The term life insurance cost for all 60-year-old male non-smokers' insurance policies 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 30

Question 31

Find $\mathrm { z } _ { \alpha / 2 }$ for the given value of $\alpha$ .
$\alpha = 0.14$

A) 1.48
B) 1.08
C) 0.14
D) 1.58

Question 32

What is the confidence coefficient in a 95% confidence interval for μ?

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

Question 33

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded a mean nicotine content of 24.5 milligrams and standard deviation of 2.3 milligrams for a sample of n = 82 cigarettes. Find a 95% confidence interval for μ.

Question 34

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. $$\begin{array} { l l c c c c r } \text { Variable } & \mathrm { N } & \text { Lo 95\% CI } & \text { Mean } & { \text { Up 95\% CI } } & \text { SD } \\\text { Parking Time } & 338 & 9.1944 & 10.466 & 11.738 & 11.885\end{array}$$
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) 95% of the observations in the population will fall within the endpoints of the interval.
C) In repeated sampling, 95% of the population means will fall within the interval created.
D) In repeated sampling, 95% of the intervals created will contain the population mean.

Question 35

How much money does the average professional football fan spend on food at a single football game? That question was posed to 40 randomly selected football fans. The sample results provided a sample mean and standard deviation of $11.00 and $2.80, respectively. Find and interpret a 99% confidence interval for μ.

Question 36

A random sample of n = 100 measurements was selected from a population with unknown mean μ and standard deviation σ. Calculate a 95% confidence interval if

Question 37

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 μ. How many of the 100 confidence intervals would you expect to actually contain μ?

Question 38

Question 39

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.

Question 40

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. $$\begin{array} { l l c c c c r } \text { Variable } & \mathrm { N } & \text { Lo 95\% CI } & \text { Mean } & { \text { Up 95\% CI } } & \text { SD } \\\text { Parking Time } & 338 & 9.1944 & 10.466 & 11.738 & 11.885\end{array}$$ Give a practical interpretation for the 95% confidence interval given above.

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

Question 41

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is invested in a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of eight private colleges in the United States revealed the following endowments (in millions of dollars): 64.5, 55.1, 232.8, 496.1, 127.6, 186.4, 104.7, and 212.2. What value will be used as the point estimate for the mean endowment of all private colleges in the United States?

A) 184.925
B) 1479.4
C) 211.343
D) 8

Question 42

Question 43

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

Question 44

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 45

Find the value of $$t _ { 0 } \text { such that the following statement is true: } P \left( - t _ { 0 } \leq t \leq t _ { 0 } \right) = .90 \text { where } \mathrm { df } = 14 \text {. }$$

A) 1.761
B) 1.345
C) 2.145
D) 2.624

Question 46

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

Question 47

Fifteen SmartCars were randomly selected and the highway mileage of each was noted. The analysis yielded a mean of 47 miles per gallon and a standard deviation of 5 miles per gallon. Which of the following would represent a 90% confidence interval for the average highway mileage of all SmartCars?

Question 48

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 for the mean was calculated to be ($2,181,260, $5,836,180). Explain what the phrase "90% confident" means.

A) In repeated sampling, 90% of the intervals constructed would contain μ.
B) 90% of the population values will fall within the interval.
C) 90% of the sample means from similar samples fall within the interval.
D) 90% of the similarly constructed intervals would contain the value of the sample mean.

Question 49

Find the value of $$t _ { 0 } \text { such that the following statement is true: } P \left( - t _ { 0 } \leq t \leq t _ { 0 } \right) = .95 \text { where } \mathrm { df } = 15 \text {. }$$

A) 2.131
B) 1.753
C) 2.602
D) 2.947

Question 50

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 97% confidence interval for the mean was calculated to be ($2,181,260, $5,836,180). What would happen to the confidence interval if the confidence level were changed to 95%?

A) The interval would get narrower.
B) The interval would get wider.
C) There would be no change in the width of the interval.
D) It is impossible to tell until the 95% interval is constructed.

Question 51

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 99% 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 $12,380 with a standard deviation of $800. What is the 99% confidence interval for the true mean resale value of a 5- year-old car of this model?

Question 52

How much money does the average professional football fan spend on food at a single football game? That question was posed to 10 randomly selected football fans. The sample results provided a sample mean and standard deviation of $19.00 and $2.95, respectively. Use this information to construct a 98% confidence interval for the mean.

Question 53

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 98% 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 population of total compensations of CEOs in the service industry is approximately normally distributed.
B) None. The Central Limit Theorem applies.
C) The sample standard deviation is less than the degrees of freedom.
D) The distribution of the sample means is approximately normal.

Question 54

Let t0 be a specific value of t. Find t0 such that the following statement is true: $$P \left( t \geq t _ { 0 } \right) = .025 \text { where df } = 20 \text {. }$$

A) 2.086
B) -2.086
C) 2.093
D) -2.093

Question 55

Suppose you selected a random sample of n = 29 measurements from a normal distribution. Compare the standard normal z value with the corresponding t value for a 95% confidence interval.

Question 56

A random sample of n = 144 measurements was selected from a population with unknown mean μ and standard deviation σ. Calculate a 90% confidence interval if

Question 57

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 t-value with 19 degrees of freedom was used.
B) In construction of the confidence interval, a t-value with 20 degrees of freedom was used.
C) In construction of the confidence interval, a z-value was used.
D) In construction of the confidence interval, a z-value with 20 degrees of freedom was used. 2 Use t-Distribution

Question 58

A random sample of 80 observations produced a mean a. Find a 90% confidence interval for the population mean μ. b. Find a 95% confidence interval for μ. c. Find a 99% confidence interval for μ. 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? 7.3 Confidence Interval for a Population Mean: Student's t-Statistic 1 Compare t-Distribution to Normal Distribution

Question 59

Find the value of $$t _ { 0 } \text { such that the following statement is true: } P \left( - t _ { 0 } \leq t \leq t _ { 0 } \right) = .99 \text { where } \mathrm { df } = 9 \text {. }$$

A) 3.250
B) 2.2821
C) 2.262
D) 1.833

Question 60

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 90% 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 $12,320 with a standard deviation of $600. Suppose that the interval is calculated to be ($12,065.92, $12,574.08). How could we alter the sample size and the confidence coefficient in order to guarantee a decrease in the width of the interval?

A) Increase the sample size but decrease the confidence coefficient.
B) Increase the sample size and increase the confidence coefficient.
C) Keep the sample size the same but increase the confidence coefficient.
D) Decrease the sample size but increase the confidence coefficient.

Question 61

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). The researcher claimed that the average GPA of all male students exceeded 2.94. Using the confidence interval supplied above, how do you respond to this claim?

A) We are 95% confident that the researcher is correct.
B) We are 100% confident that the researcher is incorrect.
C) We are 95% confident that the researcher is incorrect.
D) We cannot make any statement regarding the average GPA of male university students at the 95% confidence level.

Question 62

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 63

A marketing research company is estimating which of two soft drinks college students prefer. A random sample of 157 college students produced the following confidence interval for the proportion of college students who prefer drink A: (.344, .494). Is this a large enough sample for this analysis to work?

Question 64

For n = 800 and = .99, is the sample size large enough to construct a confidence for p?

Question 65

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded mean nicotine content of 28.4 milligrams and standard deviation of 2.2 milligrams for a sample of n = 9 cigarettes. Construct a 98% confidence interval for the mean nicotine content of this brand of cigarette.

Question 66

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. $$X=\text { sale price }$$
$$\begin{array}{r}\text {SAMPLE MEAN OF X \( =\quad 46,400 \)}\\\text {SAMPLE STANDARD DEV \( =13,747 \)}\\\text {SAMPLE SIZE OF X \( =15 \)}\\\text {CONFIDENCE \( =\quad 98 \)}\\\\\text {UPPER LIMIT \( =\quad 55,713.8 \)}\\\text {SAMPLE MEAN OF \( X=46,400 \)}\\\text {LOWER LIMIT \( =37.086 .2 \)} \end{array}$$
At what level of reliability is the confidence interval made?

A) 98%
B) 2%
C) 49%
D) 51%

Question 67

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. A friend suggests that the mean sale price of homes in this neighborhood is $42,000. Comment on your friend's suggestion.

Question 68

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?

Question 69

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 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Give a practical interpretation of the confidence interval.

Question 70

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. $$X=\text { sale price }$$
$$\begin{array}{r}\text {SAMPLE MEAN OF X \( =\quad 46,400 \)}\\\text {SAMPLE STANDARD DEV \( =13,747 \)}\\\text {SAMPLE SIZE OF X \( =15 \)}\\\text {CONFIDENCE \( =\quad 98 \)}\\\\\text {UPPER LIMIT \( =\quad 52,850.6 \)}\\\text {SAMPLE MEAN OF \( X=46,600 \)}\\\text {LOWER LIMIT \( =40,349.4 \)} \end{array}$$

Which of the following is a practical interpretation of the interval above?

A) We are 90% confident that the mean sale price of all homes in this neighborhood falls between $40,349.40 and $52,850.60.
B) We are 90% confident that the true sale price of all homes in this neighborhood fall between $40,349.40 and $52,850.60.
C) 90% of the homes in this neighborhood have sale prices that fall between $40,349.40 and $52,850.60.
D) All are correct practical interpretations of this interval.

Question 71

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 μ.

Question 72

A marketing research company is estimating which of two soft drinks college students prefer. A random sample of 341 college students produced the following 95% confidence interval for the proportion of college students who prefer one of the colas: (.341, .451). What additional assumptions are necessary for the interval to be valid?

A) No additional assumptions are necessary.
B) The sample proportion equals the population proportion.
C) The sample was randomly selected from an approximately normal population.
D) The population proportion has an approximately normal distribution.

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 for the proportion of college students who prefer American automobiles. SAMPLE PROPORTION = .396226 SAMPLE SIZE = 159 UPPER LIMIT = .46418 LOWER LIMIT = .331125 Is the sample large enough for the interval to be valid?

Question 74

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). What assumption is necessary for the confidence interval analysis to work properly?

A) The Central Limit theorem guarantees that no assumptions about the population are necessary.
B) The population that we are sampling from needs to be a t-distribution with n-1 degrees of freedom.
C) The sampling distribution of the sample mean needs to be approximately normally distributed.
D) The population that we are sampling from needs to be approximately normally distributed.

Question 75

181.387

Question 76

For n = 40 and = .35, is the sample size large enough to construct a confidence for p?

Question 77

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 $12,700 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 78

For n = 40 and = .45, is the sample size large enough to construct a confidence for p?

Question 79

The following sample of 16 measurements was selected from a population that is approximately normally distributed. Construct a 90% confidence interval for the population mean.

Question 80

A computer package was used to generate the following printout for estimating the mean sale price of homes in a particular neighborhood. $$X=\text { sale price }$$
$$\begin{array}{r}\text {SAMPLE MEAN OF X \( =\quad 46,600 \)}\\\text {SAMPLE STANDARD DEV \( =13,747 \)}\\\text {SAMPLE SIZE OF X \( =15 \)}\\\text {CONFIDENCE \( =\quad 95 \)}\\\\\text {UPPER LIMIT \( =\quad 54,213.60 \)}\\\text {SAMPLE MEAN OF \( X=46,600 \)}\\\text {LOWER LIMIT \( =38,986.40 \)} \end{array}$$

A friend suggests that the mean sale price of homes in this neighborhood is $44,000. Comment on your friend's suggestion.

A) Based on this printout, all you can say is that the mean sale price might be $44,000.
B) Your friend is wrong, and you are 95% certain.
C) Your friend is correct, and you are 95% certain.
D) Your friend is correct, and you are 100% certain.