Lightning Deaths Listed below are the numbers of deaths from lightning strikes in the United States each year for a sequence of recent and consecutive years. Find the values of the indicated statistics.

46 51 44 51 43 32 38 48 45 27 34 29 26 28 23 26 28 40 16 20

f. What important feature of the data is not revealed from an examination of the statistics, and what tool would be helpful in revealing it? What does a quick examination of the data reveal?

Lightning Deaths Listed below are the numbers of deaths from lightning strikes in the United States each year for a sequence of recent and consecutive years. Find the values of the indicated statistics.

46 51 44 51 43 32 38 48 45 27 34 29 26 28 23 26 28 40 16 20

c. standard deviation

Lightning Deaths Listed below are the numbers of deaths from lightning strikes in the United States each year for a sequence of recent and consecutive years. Find the values of the indicated statistics.

46 51 44 51 43 32 38 48 45 27 34 29 26 28 23 26 28 40 16 20

d. Variance

Lightning Deaths Listed below are the numbers of deaths from lightning strikes in the United States each year for a sequence of recent and consecutive years. Find the values of the indicated statistics.

46 51 44 51 43 32 38 48 45 27 34 29 26 28 23 26 28 40 16 20

e. Range

Lightning Deaths Based on the results given in Cumulative Review Exercise 6, assume that for a randomly selected lightning death, there is a 0.8 probability that the victim is a male.

a. Find the probability that three random people killed by lightning strikes are all males.

Hypothesis Test for Lightning Deaths Refer to the sample data given in Cumulative Review Exercise 1 and consider those data to be a random sample of annual lightning deaths from recent years. Use those data with a 0.01 significance level to test the claim that the mean number of annual lightning deaths is less than the mean of 72.6 deaths from the 1980s. If the mean is now lower than in the past, identify one of the several factors that could explain the decline.

Discarded Plastic Data Set 42 “Garbage Weight” includes weights (pounds) of discarded plastic from 62 different households. Those 62 weights have a mean of 1.911 pounds and a standard deviation of 1.065 pounds. We want to use a 0.05 level of significance to test the claim that this sample is from a population with a mean less than 2.000 pounds. Identify the null hypothesis and alternative hypothesis.

Discarded Plastic Find the test statistic used for the hypothesis test described in Exercise 1.

Discarded Plastic

What distribution is used for the hypothesis test described in Exercise 1?

For the hypothesis test described in Exercise 1, is it necessary to determine whether the 62 weights appear to be from a population having a normal distribution? Why or why not?

Discarded Plastic The P-value for the hypothesis test described in Exercise 1 is 0.2565.

What should be concluded about the null hypothesis?

What is the final conclusion that addresses the original claim?

Robust Explain what is meant by the statements that the t test for a claim about μ is robust, but the (chi)^2 test for a claim about σ is not robust.

Lightning Deaths The graph in Cumulative Review Exercise 5 was created by using data consisting of 242 male deaths from lightning strikes and 64 female deaths from lightning strikes. Assume that these data are randomly selected lightning deaths and proceed to test the claim that the proportion of male deaths is greater than . Use a 0.01 significance level. Any explanation for the result?

Job Search A Gallup poll of 195,600 employees showed that 51% of them were actively searching for new jobs. Use a 0.01 significance level to test the claim that the majority of employees are searching for new jobs

Type I Error and Type II Error

a. In general, what is a type I error? In general, what is a type II error?

Perception and Reality In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won (based on data from ICR Survey Research Group). Use a 0.05 significance level to test the claim that among all voters, the percentage who believe that they voted for the winning candidate is equal to 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions?

Test Statistics

In Exercises 9–12, refer to the exercise identified and find the value of the test statistic. (Refer to Table 8-2 to select the correct expression for evaluating the test statistic.)

Exercise 5 “Landline Phones”

Final Conclusions

In Exercises 21–24, use a significance level of α = 0.05 and use the given information for the following:

State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)

Without using technical terms or symbols, state a final conclusion that addresses the original claim

Original claim: More than 35% of air travelers would choose another airline to have access to inflight Wi-Fi. The hypothesis test results in a P-value of 0.00001.

Final Conclusions

In Exercises 21–24, use a significance level of α = 0.05 and use the given information for the following:

State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)

Without using technical terms or symbols, state a final conclusion that addresses the original claim.

Original claim: The mean pulse rate (in beats per minute) of adult males is 72 bpm. The hypothesis test results in a P-value of 0.0095.

Type I and Type II Errors

In Exercises 25–28, provide statements that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.)

The proportion of people who write with their left hand is equal to 0.1.

Type I and Type II Errors

In Exercises 25–28, provide statements that identify the type I error and the type II error that correspond to the given claim. (Although conclusions are usually expressed in verbal form, the answers here can be expressed with statements that include symbolic expressions such as p = 0.1.)

The proportion of drivers who make angry gestures is greater than 0.25.

Interpreting Power Chantix (varenicline) tablets are used as an aid to help people stop smoking. In a clinical trial, 129 subjects were treated with Chantix twice a day for 12 weeks, and 16 subjects experienced abdominal pain (based on data from Pfizer, Inc.). If someone claims that more than 8% of Chantix users experience abdominal pain, that claim is supported with a hypothesis test conducted with a 0.05 significance level. Using 0.18 as an alternative value of p, the power of the test is 0.96. Interpret this value of the power of the test.

Identifying H0 and H1

In Exercises 5–8, do the following:

a. Express the original claim in symbolic form.

b. Identify the null and alternative hypotheses.

Light Year Claim: Most adults know that a light year is a measure of distance. Sample data: A Pew Research Center survey of 3278 adults showed that 72% knew that a light year is a measure of distance.

Identifying H0 and H1

In Exercises 5–8, do the following:

a. Express the original claim in symbolic form.

b. Identify the null and alternative hypotheses.

Systolic Blood Pressure Claim: Healthy adults have systolic blood pressure levels with a standard deviation greater than 5 mm Hg. Sample data: Data Set 1 “Body Data” in Appendix B shows that for 300 healthy adults, the systolic blood pressure amounts have a standard deviation of 15.85 mm Hg.

Finding P-Values

In Exercises 13–16, do the following:

i. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

ii. Find the P-value. (See Figure 8-3.)

iii. Using a significance level of α = 0.05 should we reject H0 or should we fail to reject H0?

The test statistic of z = -0.75 is obtained when testing the claim that p<1/3.

Finding P-Values

In Exercises 13–16, do the following:

i. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

ii. Find the P-value. (See Figure 8-3.)

iii. Using a significance level of α = 0.05 should we reject H0 or should we fail to reject H0?

The test statistic of z = -1.60 is obtained when testing the claim that p ≠ 0.455.

Finding Critical Values

In Exercises 17–20, refer to the information in the given exercise and use a 0.05 significance level for the following.

a. Find the critical value(s).

b. Should we reject H0 or should we fail to reject H0?

Exercise 15

Finding Critical Values

In Exercises 17–20, refer to the information in the given exercise and use a 0.05 significance level for the following.

a. Find the critical value(s).

b. Should we reject H0 or should we fail to reject H0?

Exercise 16

Estimates vs. Hypothesis Tests Labels on cans of Dr. Pepper soda indicate that they contain 12 oz of the drink. We could collect samples of those cans and accurately measure the actual contents, then we could use methods of Section 7-2 for making an estimate of the mean amount of Dr. Pepper in cans, or we could use those measured amounts to test the claim that the cans contain a mean of 12 oz. What is the difference between estimating the mean and testing a hypothesis about the mean?

Interpreting P-value The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of p > 0.5 which corresponds to the claim that the method increases the likelihood of having a girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the method, which of the following P-values would you prefer as a result in your hypothesis test: 0.999, 0.5, 0.95, 0.05, 0.01, 0.001? Why?

Identifying H0 and H1

In Exercises 5–8, do the following:

a. Express the original claim in symbolic form.

b. Identify the null and alternative hypotheses.

Landline Phones Claim: Fewer than 10% of homes have only a landline telephone and no wireless phone. Sample data: A survey by the National Center for Health Statistics showed that among 16,113 homes, 5.8% had landline phones without wireless phones.