Deck 6: Statistical Inference

Question 1

When the expected value of the point estimator is equal to the population parameter it estimates, it is said to be

A)unbiased.
B)precise.
C)symmetric.
D)predicted.

Answer 1

unbiased.

Question 2

The purpose of statistical inference is to make estimates or draw conclusions about a

A)sample based upon information obtained from the population.
B)population based upon information obtained from the sample.
C)statistic based upon information obtained from the population.
D)mean of the sample based upon the mean of the population.

Answer 2

population based upon information obtained from the sample.

Question 3

In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 24 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is

A)21.
B)22.
C)23.
D)24.

Answer 3

23.

Question 4

The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the estimate of the standard error of the proportion proportion $\sigma _ { \bar { p } }$ ?

A)0.039
B)0.050
C)0.350
D)0.455

Question 5

The population parameter value and the point estimate differ because a sample is not a census of the entire population, but it is being used to develop the

A)population parameter.
B)point estimate.
C)population mean.
D)standard error.

Question 6

The value of the ___________ is used to estimate the value of the population parameter.

A)population statistic
B)sample parameter
C)population estimate
D)sample statistic

Question 7

A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. What is the standard error of the mean?

A)0.900
B)2.876
C)3.061
D)4.743

Question 8

As the number of degrees of freedom for a t distribution increases, the difference between the t distribution and the standard normal distribution

A)becomes larger.
B)becomes smaller.
C)stays the same.
D)fluctuates.

Question 9

The basis for using a normal probability distribution to approximate the sampling distribution of the sample means and population mean is

A)Chebyshev's theorem.
B)the empirical rule.
C)the central limit theorem.
D)Bayes' theorem.

Question 10

An estimate of a population parameter that provides an interval of values believed to contain the value of the parameter is known as the

A)confidence level.
B)interval estimate.
C)parameter level.
D)population estimate.

Question 11

The random numbers generated using Excel's RAND function follows a __________ probability distribution between 0 and 1.

A)normal
B)uniform
C)binomial
D)random

Question 12

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size

A)N and n have the same probability of being selected.
B)n has a probability of 0.5 of being selected.
C)n has a probability of 0.05 of being selected.
D)n has the same probability of being selected.

Question 13

If the expected value of the sample statistic is equal to the population parameter being estimated, the sample statistic is said to

A)have low variability.
B)be an unbiased estimator of the population parameter.
C)have high precision.
D)be a random estimator of the population parameter.

Question 14

A simple random sample of 31 observations was taken from a large population. The sample mean equals 5. Five is a

A)population parameter.
B)point estimate.
C)population mean.
D)standard error.

Question 15

The t value for a 99% confidence interval estimation based upon a sample of size 10 is

A)1.645.
B)1.812.
C)2.576.
D)3.169.

Question 16

The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the point estimate of the proportion of the population that logged onto Facebook that day?

A)0.25
B)0.35
C)0.53
D)0.65

Question 17

In interval estimation, as the sample size becomes larger, the interval estimate

A)becomes narrower.
B)becomes wider.
C)remains the same, since the mean is not changing.
D)gets closer to 1.96.

Question 18

A random sample selected from an infinite population is a sample selected such that each element selected comes from the same __________ and each element is selected __________.

A)population; independently
B)population; simultaneously
C)sample; independently
D)sample; simultaneously

Question 19

The finite correction factor should be used in the computation of the standard deviation of the sample mean and the standard population when n / N is

A)greater than 0.05.
B)greater than 0.5.
C)less than 0.05.
D)less than 0.5.

Question 20

For a population with an unknown distribution, the form of the sampling distribution of the sample mean is

A)approximately normal for small sample sizes.
B)exactly normal for large sample sizes.
C)exactly normal for small sample sizes.
D)approximately normal for large sample sizes.

Question 21

A sample of 37 AA batteries had a mean lifetime of 584 hours. A 95% confidence interval for the population mean was 579.2 < μ < 588.8. Which statement is the correct interpretation of the results?

A)We are 95% confident that the mean lifetime of all the bulbs in the population is between 579.2 hours and 588.8 hours.
B)The probability that the population mean is between 579.2 hours and 588.8 hours is 0.95.
C)95% of the light bulbs in the sample had lifetimes between 579.2 hours and 588.8 hours.
D)None of these statements correctly interpret the results.

Question 22

The owners of a fast food restaurant have automatic drink dispensers to help fill orders more quickly. When the 12 ounce button is pressed, they would like for exactly 12 ounces of beverage to be dispensed. There is, however, some variation in this amount. The company does not want the machine to systematically over fill or under fill the cups. Which of the following gives the correct set of hypotheses?

A)H₀: u > 12, H_a: u < 12
B)H₀: u = 12, H_a: u ≠ 12
C)H₀: u ≤ 12, H_a: u > 12
D)H₀: u ≥ 12, H_a: u < 12

Question 23

A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. The 95% confidence interval for the true mean number of pushups that can be done is ​

A)5.75 to 24.25.
B)8.56 to 21.40.
C)11.31 to 18.55.
D)13.02 to 16.98.

Question 24

A pizza shop advertises that they deliver in 30 minutes or less or it is free. People who live in homes that are located on the opposite side of town believe it will take the pizza shop longer than 30 minutes to make and deliver the pizza. Write the null and alternative hypotheses that can be used to conduct a significance test.

A)H₀: u ≤ 30, H_a: u > 30
B)H₀: u < 30, H_a: u > 30
C)H₀: u ≥ 30, H_a: u < 30
D)H₀: u > 30, H_a: u < 30

Question 25

Using an α = 0.04, a confidence interval for a population proportion is determined to be 0.65 to 0.75. If the level of significance is decreased, the interval for the population proportion

A)becomes narrower.
B)becomes wider.
C)does not change.
D)remains the same.

Question 26

A null and alternative hypothesis for a one proportion z test are given as H₀: p = 0.8, H_a: p < 0.8. This hypothesis test is

A)lower-tailed.
B)upper-tailed.
C)two-tailed.
D)these hypotheses are incorrectly stated.

Question 27

Two approaches to drawing a conclusion in a hypothesis test are

A)p-value and critical value.
B)one-tailed and two-tailed.
C)Type I and Type II.
D)null and alternative.

Question 28

A Type I error is committed when

A)a true alternative hypothesis is not accepted.
B)a true null hypothesis is rejected.
C)the critical value is greater than the value of the test statistic.
D)the validity of a claim was rejected.

Question 29

Larger values of α have the disadvantage of increasing the probability of making a

A)Type I error.
B)Type II error.
C)random sampling error.
D)normal probability error.

Question 30

A pizza shop advertises that they deliver in 30 minutes or less or it is free. People who live in homes that are located on the opposite side of town believe it will take the pizza shop longer than 30 minutes to make and deliver the pizza. A random sample of 50 deliveries to homes across town was taken and the mean time was computed to be 32 minutes. What is the appropriate symbol to represent the value, 32?

A)u = 32
B) $\bar { x }$ = 32
C)n = 32
D) $\bar { p }$ = 32

Question 31

The average number of hours for a random sample of mail order pharmacists from company A was 50.1 hours last year. It is believed that changes to medical insurance have led to a reduction in the average work week. To test the validity of this belief, the hypotheses are

A)H₀: u > 50.1, H_a: u < 50.1.
B)H₀: u = 50.1, H_a: u = 50.1.
C)H₀: u ≤ 50.1, H_a: u > 50.1.
D)H₀: u ≥ 50.1, H_a: u < 50.1.

Question 32

In a random sample of 400 registered voters, 120 indicated they plan to vote for Trump for President. Determine a 95% confidence interval for the proportion of all the registered voters who will vote for Trump.

A)(0.25, 0.34)
B)(0.27, 0.32)
C)(0.29, 0.30)
D)Cannot be determined from the information given.

Question 33

The proportion of dental procedures that are extractions is 0.16. Which of the following exemplifies a Type I error in this situation?

A)We reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually different from 0.16.
B)We fail to reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually 0.16.
C)We reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually 0.16.
D)We fail to reject the claim that the proportion of dental procedures that are extractions is 0.16 when the proportion is actually different from 0.16.

Question 34

A large manufacturing plant has analyzed the amount of time required to produce an electrical part and determined that the times follow a normal distribution with mean time ? = 45 hours. The production manager has developed a new procedure for producing the part. He believes that the new procedure will decrease the population mean amount of time required to produce the part. After training a group of production line workers, a random sample of 25 parts will be selected and the average amount of time required to produce the parts will be determined. If the switch is made to the new procedure, the cost to implement the new procedure will be more than offset by the savings in manpower required to produce the parts. Use the hypotheses: H_o: ? ? 45 hours and H_a: ? < 45 hours. Determine the p value of the test statistic if the sample mean amount of time is $\bar { x }$ = 43.118 hours with the sample standard deviation s = 5.5 hours.

A)0.04973
B)0.04999
C)0.95818
D)0.04354

Question 35

A large manufacturing plant has analyzed the amount of time required to produce an electrical part and determined that the times follow a normal distribution with mean time ? = 45 hours. The production manager has developed a new procedure for producing the part. He believes that the new procedure will decrease the population mean amount of time required to produce the part. After training a group of production line workers, a random sample of 25 parts will be selected and the average amount of time required to produce them will be determined. If the switch is made to the new procedure, the cost to implement the new procedure will be more than offset by the savings in manpower required to produce the parts. Use the hypotheses: H₀: ? ? 45 hours and H_a: ? < 45 hours. If the sample mean amount of time is $\bar { x }$ = 43.118 hours with the sample standard deviation s = 5.5 hours, give the appropriate conclusion, for ? = 0.025. ?

A)Do not reject H₀, do not switch to the new procedure.
B)Reject H₀, switch to the new procedure.
C)Reject H₀, do not switch to the new procedure.
D)Do not reject H₀, switch to the new procedure.

Question 36

A statistics teacher started class one day by drawing the names of 10 students out of a hat and asked them to do as many pushups as they could. The 10 randomly selected students averaged 15 pushups per person with a standard deviation of 9 pushups. Suppose the distribution of the population of number of pushups that can be done is approximately normal. If we would like to capture the population mean with 95% confidence the margin of error would be ?

A) $1.960 \left( \frac { 9 } { \sqrt { 10 } } \right)$
B) $2.125 \left( \frac { 15 } { \sqrt { 10 } } \right)$
C) $2.262 \left( \frac { 9 } { \sqrt { 10 } } \right)$
D) $3.250 \left( \frac { 15 } { \sqrt { 10 } } \right)$

Question 37

Determine whether the alternative hypothesis is left-tailed, right-tailed, or two-tailed: H₀: μ = 11, H_a: μ > 11.

A)Left-tailed
B)Right-tailed
C)Two-tailed
D)There is not enough information to make a determination.

Question 38

What are the two decisions that you can make from performing a hypothesis test?

A)Reject the null hypothesis; Fail to reject the null hypothesis
B)Accept the null hypothesis; Accept the alternative hypothesis
C)Make a Type I error; Make a Type II error
D)Reject the alternative hypothesis; Accept the null hypothesis

Question 39

The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. Compute the 95% confidence interval for the population proportion.

A) $0.35 \pm 1.96 \sqrt { \frac { 0.35 ( 1 - 0.35 ) } { 150 } }$
B) $0.35 \pm 1.645 \sqrt { \frac { 0.35 ( 1 - 0.35 ) } { 150 } }$
C) $0.53 \pm 1.645 \sqrt { \frac { 0.53 ( 1 - 0.53 ) } { 150 } }$
D) $0.53 \pm 1.96 \sqrt { \frac { 0.53 ( 1 - 0.53 ) } { 150 } }$

Question 40

A one-tailed test is a hypothesis test in which the rejection region is

A)in both tails of the sampling distribution.
B)in one tail of the sampling distribution.
C)only in the lower tail of the sampling distribution.
D)only in the upper tail of the sampling distribution.

Question 41

Statistical significance at the 0.01 level is ___________ than significance at the 0.05 level.

A)more difficult to achieve
B)easier to achieve
C)less costly
D)less informative

Question 42

The medical director of a company looks at the medical records of all 50 employees and finds that the mean systolic blood pressure for these employees is 126.07. The value of 126.07 is symbolized by

Question 43

Which statement is NOT true?

A)Rejecting the null hypothesis when it is true is a Type I error.
B)The probability of making a Type I error is symbolized by α.
C)Failing to reject the null hypothesis when it is false is a Type I error.
D)Type II error can occur for both one and two-tailed tests.

Question 44

Which statement is NOT true?

A)The greater the level of confidence, the more likely it is that the confidence interval actually includes the true population mean.
B)The greater the level of confidence, the larger the z-score.
C)The greater the level of confidence, the wider the confidence interval.
D)Rejecting the null hypothesis when it is true is a Type II error.

Question 45

In a survey of 3539 female university students ages 18-22, 401 say they live in off-campus housing. If you constructed 90% and 95% confidence intervals for the population proportion, how would they differ? As the level of confidence __________, the confidence interval gets __________.

Question 46

You are __________ to commit a Type I error using the 0.05 level of significance than using the 0.01 level of significance.

A)more likely
B)less likely
C)equally likely
D)twice as likely

Question 47

A student wants to determine if pennies are really fair when flipped, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. If p denotes the true probability of a penny landing heads up when flipped, what are the appropriate null and alternative hypotheses?

A)H₀: p ≥ 0.5, H_a: p < 0.5.
B)H₀: p ≤ 0.5, H_a: p ≠ 0.5.
C)H₀: p = 0.5, H_a: p ≠ 0.5.
D)H₀: p ≥ 28, H_a: p < 28.