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Chapter 8: Q3 (page 382)

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.

Equivalence of Methods If we use the same significance level to conduct the hypothesis test using the P-value method, the critical value method, and a confidence interval, which method is not equivalent to the other two?

Short Answer

Expert verified

The confidence interval method is not equivalent to the p-value, and the critical value methods

Step by step solution

01

Given information

It is given that out of 510 people who responded to a survey, 53% said 鈥測es鈥� to the question of whether they should replace passwords with biometric security.

02

Equivalence of methods

Let the level of significance be 伪.

The p-value and the critical value method that can be used to test the given claim utilizes a z-score value with the level of significance equal to role="math" localid="1648623739821" 伪.

The confidence interval method that can be used to test the given claim utilizes a z-score value at role="math" localid="1648623747432" 伪2the significance level.

Thus, the confidence interval method is not equivalent to the p-value and the critical value methods.

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Most popular questions from this chapter

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?

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.

Tennis Instant Replay The Hawk-Eye electronic system is used in tennis for displaying an instant replay that shows whether a ball is in bounds or out of bounds so players can challenge calls made by referees. In a recent U.S. Open, singles players made 879 challenges and 231 of them were successful, with the call overturned. Use a 0.01 significance level to test the claim that fewer than 1/ 3 of the challenges are successful. What do the results suggest about the ability of players to see calls better than referees?

Critical Values. In Exercises 21鈥�24, refer to the information in the given exercise and do the following.

a. Find the critical value(s).

b. Using a significance level of 伪= 0.05, should we reject H0or should we fail to reject H0?

Exercise 19

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 7 鈥淧ulse Rates鈥�

Lead in Medicine Listed below are the lead concentrations (in ) measured in different Ayurveda medicines. Ayurveda is a traditional medical system commonly used in India. The lead concentrations listed here are from medicines manufactured in the United States (based on data from 鈥淟ead, Mercury, and Arsenic in US and Indian Manufactured Ayurvedic Medicines Sold via the Internet,鈥� by Saper et al., Journal of the American Medical Association,Vol. 300, No. 8). Use a 0.05 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 渭g/g.

3.0 6.5 6.0 5.5 20.5 7.5 12.0 20.5 11.5 17.5
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