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Chapter 8: Q7CQQ (page 356)

Uncertainty True or false: If correct methods of hypothesis testing are used with a large simple random sample that satisfies the test requirements, the conclusion will always be true.

Short Answer

Expert verified

It is false that after applying the correct method to test a claim with a sufficiently large sample, it will always result in a conclusion that is true.

Step by step solution

01

Given information

The following statement is considered:

If correct methods of hypothesis testing are used with a large simple random sample that satisfies the test requirements, the conclusion will always be true.

02

Conclusion of the test

The statement “the conclusion will always be true” denotes the rejection of the null hypothesis.

The conclusion of a hypothesis test depends on the characteristics of the data values of the sample.

A sufficiently large sample may have statistics that are quite extreme which can result in a very small p-value and hence, the rejection of the null hypothesis.

Conversely, if the sample is large, but the p-value comes out to be greater than the significance level, then the null hypothesis is failed to reject.

Therefore, even if the sample follows all the requirements, there can be a case of failure to reject the null hypothesis, and thus, the conclusion will not be true.

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Most popular questions from this chapter

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.

Airport Data Speeds Data Set 32 “Airport Data Speeds” 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 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.

Store Checkout-Scanner Accuracy In a study of store checkout-scanners, 1234 items were checked for pricing accuracy; 20 checked items were found to be overcharges, and 1214 checked items were not overcharges (based on data from “UPC Scanner Pricing Systems: Are They Accurate?” by Goodstein, Journal of Marketing, Vol. 58). Use a 0.05 significance level to test the claim that with scanners, 1% of sales are overcharges. (Before scanners were used, the overcharge rate was estimated to be about 1%.) Based on these results, do scanners appear to help consumers avoid overcharges?

Confidence interval Assume that we will use the sample data from Exercise 1 “Video Games” with a 0.05 significance level in a test of the claim that the population mean is greater than 90 sec. If we want to construct a confidence interval to be used for testing the claim, what confidence level should be used for the confidence interval? If the confidence interval is found to be 21.1 sec < μ< 191.4 sec, what should we conclude about the claim?

In Exercises 9–12, 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 6 “Cell Phone”

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

a. Find the critical value(s).

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

Exercise 19
See all solutions

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