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Chapter 8: Q. 9.65 (page 370)
Determine the sufficient evidence to reject the null hypothesis in favor of alternative hypothesis.
(a) z= -0.74 (b) z= 1.16
(a) The P-value is 0.22965
(b) The P-value is 0.87698
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Technology. In Exercises 9鈥�12, test the given claim by using the display provided from technology. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.
Airport Data Speeds Data Set 32 鈥淎irport Data Speeds鈥� in Appendix B includes Sprint data speeds (mbps). The accompanying TI-83/84 Plus display results from using those data to test the claim that they are from a population having a mean less than 4.00 Mbps. Conduct the hypothesis test using these results.
Testing Hypotheses. In Exercises 13鈥�24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.
Cans of Coke Data Set 26 鈥淐ola Weights and Volumes鈥� in Appendix B includes volumes (ounces) of a sample of cans of regular Coke. The summary statistics are n = 36, x = 12.19 oz, s = 0.11 oz. Use a 0.05 significance level to test the claim that cans of Coke have a mean volume of 12.00 ounces. Does it appear that consumers are being cheated?
In Exercises 1鈥�4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: 鈥淪hould Americans replace passwords with biometric security (fingerprints, etc)?鈥� Among the respondents, 53% said 鈥測es.鈥� We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.
Requirements and Conclusions
a. Are any of the three requirements violated? Can the methods of this section be used to test the claim?
b. It was stated that we can easily remember how to interpret P-values with this: 鈥淚f the P is low, the null must go.鈥� What does this mean?
c. Another memory trick commonly used is this: 鈥淚f the P is high, the null will fly.鈥� Given that a hypothesis test never results in a conclusion of proving or supporting a null hypothesis, how is this memory trick misleading?
d. Common significance levels are 0.01 and 0.05. Why would it be unwise to use a significance level with a number like 0.0483?
Testing Claims About Proportions. In Exercises 9鈥�32, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value, or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim. Use the P-value method unless your instructor specifies otherwise. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section.
Postponing Death An interesting and popular hypothesis is that individuals can temporarily postpone death to survive a major holiday or important event such as a birthday. In a study, it was found that there were 6062 deaths in the week before Thanksgiving, and 5938 deaths the week after Thanksgiving (based on data from 鈥淗olidays, Birthdays, and Postponement of Cancer Death,鈥� by Young and Hade, Journal of the American Medical Association, Vol. 292, No. 24). If people can postpone death until after Thanksgiving, then the proportion of deaths in the week before should be less than 0.5. Use a 0.05 significance level to test the claim that the proportion of deaths in the week before Thanksgiving is less than 0.5. Based on the result, does there appear to be any indication that people can temporarily postpone death to survive the Thanksgiving holiday?
In Exercises 9鈥�12, refer to the exercise identified. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favours 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 favours heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).
Exercise 5 鈥淥nline Data鈥�
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