Exam 3

The minimum sample size n required to estimate a population mean with 95% confidence and the desired margin of error 1.5 was found to be 198. Which of the following is the approximate value of the assumed estimate of the population standard deviation? a. 10.7690 b. 12.8309 c. 115.9671 d. 164.6326

a. 10.7690

Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. Which of the following supports this when selecting sample sizes? a. A larger sample size reduces the margin of error. b. A smaller sample size reduces the margin of error. c. A larger sample size increases the margin of error. d. A sample size has no impact on the margin of error.

a. A larger sample size reduces the margin of error.

The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district's claim, how does one define the population parameter of interest? a. The mean score on the eighth-grade reading comprehension test b. The number of eighth graders who took the reading comprehension test c. The standard deviation of the score on the eighth-grade reading comprehension test d. The proportion of eighth graders who scored above 73 on the reading comprehension test

a. The mean score on the eighth-grade reading comprehension test

Which of the following are two-tailed tests? Multiple Choice Ho:μ ≤ 10, HA:μ > 10 Ho:μ = 10, HA:μ ≠ 10 Ho:μ ≥ 400, HA:μ < 400 Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400

Ho:μ = 10, HA:μ ≠ 10

What is the decision rule when using the p-value approach to hypothesis testing? a. Reject Ho if the p-value > α. b. Reject Ho if the p-value < α. c. Do not reject Ho if the p-value < 1 - α. d. Do not reject Ho if the p-value > 1 - α.

b. Reject Ho if the p-value < α.

A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids." a. Type I: 4%, Type II: 6% b. Type I: 6%, Type II: 4% c. Type I: 94%, Type II: 4% d. Type I: 4%, Type II: 94%

a. Type I: 4%, Type II: 6%

A random sample of 130 mortgages in the state of Maryland was randomly selected. From this sample, 14 were found to be delinquent on their current payment. The 98% confidence interval for the proportion based on this sample is _______. a. [0.044, 0.171] b. [0.036, 0.180] c. [0.029, 0.188] d. [0.015, 0.201]

a. [0.044, 0.171]

A basketball coach wants to know how many free throws an NBA player shoots during the course of an average practice. The coach takes a random sample of 43 players and finds the average number of free throws shot per practice was 225 with a standard deviation of 35. Construct a 99% confidence interval for the average number of free throws in practice. a. [210.5992, 239.4008] b. [210.6155, 239.3845] c. [211.2506, 238.7494] d. [214.2290, 235.7710]

a. [210.5992, 239.4008]

If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05, then the correct conclusion is to ________________. a. reject the null hypothesis b. not reject the null hypothesis c. reject the null hypothesis if σ = 10 d. not reject the null hypothesis if σ = 10

a. reject the null hypothesis

To test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the value of the test statistic is computed as t29 = 2.42 If we choose a 5% significance level, we _____________. a. reject the null hypothesis and conclude that the mean IQ is greater than 100 b. reject the null hypothesis and conclude that the mean IQ is not greater than 100 c. do not reject the null hypothesis and conclude that the mean IQ is greater than 100 d. do not reject the null hypothesis and conclude that the mean IQ is not greater than 100

a. reject the null hypothesis and conclude that the mean IQ is greater than 100

A Type I error occurs when we ___________. a. reject the null hypothesis when it is actually true b. reject the null hypothesis when it is actually false c. do not reject the null hypothesis when it is actually true d. do not reject the null hypothesis when it is actually false

a. reject the null hypothesis when it is actually true

It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. When testing the two hypotheses, H0>: p ≤ 0.50 and HA: p > 0.50, p stands for _____________. a. the current proportion of babies born out of wedlock b. the mean number of babies born out of wedlock c. the number of babies born out of wedlock d. the general belief that the proportion of babies born out of wedlock is no more than 0.50

a. the current proportion of babies born out of wedlock

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. The value of the test statistic is ____________. a. z = -1.429 b. t99 = -1.429 c. z = 1.429 d. t99 = 1.429

a. z = -1.429

In an examination of holiday spending (known to be normally distributed) of a sample of 16 holiday shoppers at a local mall, an average of $54 was spent per hour of shopping. Based on the current sample, the standard deviation is equal to $21. Find a 90% confidence interval for the population mean level of spending per hour. a. [$44.83, $63.17] b. [$44.79, $63.20] c. [$45.36, $62.63] d. [$46,96, $61.04]

b. [$44.79, $63.20]

A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________. a. the franchiser builds on an acceptable site b. the franchiser builds on an unacceptable site c. the franchiser does not build on an acceptable site d. the franchiser does not build on an unacceptable site

b. the franchiser builds on an unacceptable site

A 90% confidence interval is constructed for the population mean. If a 95% confidence interval had been constructed instead (everything else remaining the same), the width of the interval would have been ________ and the probability of making an error would have been _________. a. wider; bigger b. wider; smaller c. narrower; bigger d. narrower; smaller

b. wider; smaller

Find the minimum sample size when we want to construct a 90% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a preselected poll of 100 residents, 22 supported her. The desired margin of error is 0.08. a. n = 44 b. n = 72 c. n = 73 d. n = 103

c. n = 73

How do the tdf and z distributions differ? a. There is no difference between the tdf and z distributions; they both do not have asymptomatic tails. b. The z distribution has broader tails (it is flatter around zero). c. The tdf distribution has broader tails (it is flatter around zero). d. The z distribution has asymptotic tails, while the tdf distribution does not.

c. The tdf distribution has broader tails (it is flatter around zero).

What is the purpose of calculating a confidence interval? a. To provide a range of values that has a certain large probability of containing the sample statistic of interest. b. To provide a range of values that, with a certain measure of confidence, contains the sample statistic of interest. c. To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest. d. To provide a range of values that has a certain large probability of containing the population parameter of interest.

c. To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest.

We draw a random sample of size 25 from the normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean? a. [11.2600, 13.7400] b. [11.3835, 13.6165] c. [11.7019, 13.2981] d. [11.7793, 13.2207]

c. [11.7019, 13.2981]

The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean, then _______________________________________________. a. the resulting margin of error will increase and the risk of reporting an incorrect interval will increase b. the resulting margin of error will decrease and the risk of reporting an incorrect interval will increase c. the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease d. the resulting margin of error will decrease and the risk of reporting an incorrect interval will decrease

c. the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease

What is zα / 2 z α⁢/2⁢ for a 95% confidence interval of the population mean? a. 0.48 b. 0.49 c. 1.645 d. 1.96

d. 1.96

A politician wants to estimate the percentage of people who like his new slogan. Given that no prior estimate of the population proportion is available, what is the minimum sample size such that the margin of error is no more than 0.08 for a 95% confidence interval? a. 105.70 b. 106 c. 150.06 d. 151

d. 151

What is tα/2, dftα⁢/2⁢, df for a 99% confidence interval of the population mean based on a sample of 25 observations? a.2.492 b. 2.576 c. 2.787 d. 2.797

d. 2.797

In general, the null and alternative hypotheses are __________. a. additive b. correlated c. multiplicative d. mutually exclusive

d. mutually exclusive

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is E = 1.5? The population standard deviation is known to be 10.75. a. n = 138 b. n = 139 c. n = 197 d. n = 198

d. n = 198