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Chapter 8: Q3BSC (page 356)

In Exercises 1–4, 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: “Should Americans replace passwords with biometric security (fingerprints, etc)?” Among the respondents, 53% said “yes.” 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 “yes” to the question of whether they should replace passwords with biometric security.

02

Equivalence of methods

Let the level of significance be\(\alpha \).

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\(\alpha \).

The confidence interval method that can be used to test the given claim utilizes a z-score value at\(\frac{\alpha }{2}\)the 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

The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analysed 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: 0.999, 0.5, 0.95, 0.05, 0.01, and 0.001? Why?

Identifying H0and H1. In Exercises 5–8, do the following:

a. Express the original claim in symbolic form.

b. Identify the null and alternative hypotheses.

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Estimates and Hypothesis Tests Data Set 3 “Body Temperatures” in Appendix B includes sample body temperatures. We could use methods of Chapter 7 for making an estimate, or we could use those values to test the common belief that the mean body temperature is 98.6°F. What is the difference between estimating and hypothesis testing?

Technology. In Exercises 9–12, 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.

Tornadoes Data Set 22 “Tornadoes” in Appendix B includes data from 500 random tornadoes. The accompanying StatCrunch display results from using the tornado lengths (miles) to test the claim that the mean tornado length is greater than 2.5 miles.

Testing Claims About Proportions. In Exercises 9–32, 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.

Touch Therapy Repeat the preceding exercise using a 0.01 significance level. Does the conclusion change?
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