Section 8.1 Homework

Which of the following is NOT a true statement about error in hypothesis​ testing?

A type I error is making the mistake of rejecting the null hypothesis when it is actually false.

Which of the following is NOT true about the tails in a​ distribution?

The inequality symbol in the alternative hypothesis points away from the critical region.

​Claim: Most adults would not erase all of their personal information online if they could. A software firm survey of 566 randomly selected adults showed that 0.3​% of them would erase all of their personal information online if they could. Make a subjective estimate to decide whether the results are significantly low or significantly​ high, then state a conclusion about the original claim.

The results are significantly low, so there is sufficient evidence to support the claim that most adults would not erase all of their personal information online if they could.

Make a decision about the given claim. Use only the rare event​ rule, and make subjective estimates to determine whether events are likely. For​ example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20​ flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads​ (because it is easy to get 11 heads in 20 flips by chance with a fair​ coin). ​Claim: The mean pulse rate (in beats per minute) of students in a large statistics class is less than 93. A simple random sample of the students has a mean pulse rate of 71.4.

The sample is not unusual if the claim is true. The sample is unusual if the claim is false.​ Therefore, there is sufficient evidence to support the claim.

Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 531 randomly selected adults showed that 59​% of them would erase all of their personal information online if they could. Find the value of the test statistic.

The value of the test statistic is 4.15.

​Claim: The mean pulse rate​ (in beats per​ minute) of adult males is equal to 69 bpm. For a random sample of 162 adult​ males, the mean pulse rate is 67.6 bpm and the standard deviation is 10.9 bpm. Find the value of the test statistic.

The value of the test statistic is −1.63.

​Claim: Fewer than 91% of adults have a cell phone. In a reputable poll of 1082 ​adults, 86% said that they have a cell phone. Find the value of the test statistic.

The value of the test statistic is −5.75.

Which of the following is NOT true about​ P-values in hypothesis​ testing?

The​ P-value separates the critical region from the values that do not lead to rejection of the null hypothesis.

Identify the type I error and the type II error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to 0.21.

Type I: Reject the claim that the proportion of people who write with their left hand is 0.21 when the proportion is actually 0.21. Type II: Fail to reject the claim that the proportion of people who write with their left hand is 0.21 when the proportion is actually different from 0.21.

Identify the type I error and the type II error that correspond to the given hypothesis. The percentage of high school students who graduate is less than 55%.

Type I: Reject the null hypothesis that the percentage of high school students who graduate is equal to 55% when that percentage is actually equal to 55%. Type II: Fail to reject the null hypothesis that the percentage of high school students who graduate is equal to 55% when that percentage is actually less than 55%.

Assume a significance level of α=0.05 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: MoreMore than 58​% of adults would erase all of their personal information online if they could. The hypothesis test results in a​ P-value of 0.1798. b. Without using technical​ terms, state a final conclusion that addresses the original claim. Which of the following is the correct​ conclusion?

a. Fail to reject H0 because the​ P-value is greater than α. b.There is not sufficient evidence to support the claim that the percentage of adults that would erase all of their personal information online if they could is more than 58​%.

Assume a significance level of alpha equals 0.01α=0.01 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: The standard deviation of pulse rates of a certain group of adult males is more than 14 bpm. The hypothesis test results in a​ P-value of 0.3843.

a. Fail to reject H0 because the​P-value is greater than α. b. There is not sufficient evidence to support the claim that the standard deviation of pulse rates of the group of adult males is more than 14 bpm.

Assume a significance level of α=0.01 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: The mean pulse rate​ (in beats per​ minute) of a certain group of adult males is 72 bpm. The hypothesis test results in a​ P-value of 0.0006. b. Without using technical​ terms, state a final conclusion that addresses the original claim. Which of the following is the correct​ conclusion?

a. Reject H0 because the​ P-value is less than or equal to α. b. There is sufficient evidence to warrant rejection of the claim that the mean pulse rate​ (in beats per​ minute) of the group of adult males is 72 bpm.

The test statistic of z= −2.72 is obtained when testing the claim that p < 0.54. a. Using a significance level of α= 0.10​, find the critical​ value(s). b. Should we reject H0 or should we fail to reject H0​?

a. The critical​ value(s) is/are z= −1.28. b. Reject H0. There is sufficient evidence to support the claim that p< 0.54.

The test statistic of z= 2.47 is obtained when testing the claim that p≠ 0.363. a. Identify the hypothesis test as being​ two-tailed, left-tailed, or​ right-tailed. b. Find the​ P-value. c. Using a significance level of α= 0.05​, should we reject H0 or should we fail to reject H0​?

a. This is a two-tailed test. b. P-value = 0.14 c. Reject H0. There is sufficient evidence to support the claim that p≠ 0.363.

​Claim: Most adults would erase all of their personal information online if they could. A software firm survey of 548 randomly selected adults showed that 64​% of them would erase all of their personal information online if they could. a. Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information. b. Identify the null and alternative hypotheses.

a. p > .5 b. H0​: p=.5 H1​: p > .5

The test statistic of z= 1.39 is obtained when testing the claim that p > 0.8. a. Identify the hypothesis test as being​ two-tailed, left-tailed, or​ right-tailed. b. Find the​ P-value. c. Using a significance level of α= 0.01​, should we reject H0 or should we fail to reject H0​?

a. right-tailed test b. P-value = 0.082 c. Fail to reject H0. There is not sufficient evidence to support the claim that p > 0.8.

​Claim: The mean pulse rate​ (in beats per​ minute) of adult males is equal to 68.6 bpm. For a random sample of 173 adult​ males, the mean pulse rate is 67.9 bpm and the standard deviation is 10.6 bpm. a. Express the original claim in symbolic form. b. Identify the null and alternative hypotheses.

a. μ= 68.6 bpm b. H0: μ= 68.6 bpm H1​: μ≠ 68.6 bpm

Claim: The standard deviation of pulse rates of adult males is less than 11 bpm. For a random sample of 128 adult​ males, the pulse rates have a standard deviation of 10.5 bpm. a. Express the original claim in symbolic form. b. Identify the null and alternative hypotheses.

a. σ< 11 bpm b. H0​: σ= 11 bpm H1: σ< 11 bpm

A​ _____________ is a procedure for testing a claim about a property of a population.

hypothesis test

The​ _________ hypothesis is a statement that the value of a population parameter is equal to some claimed value.

null

The ___________ is a value used in making a decision about the null hypothesis and is found by converting the sample statistic to a score with the assumption that the null hypothesis is true.

test statistic