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Chapter 9: Q3BSC (page 414)

Hypothesis Tests and Confidence Intervals for Hemoglobin

a. Exercise 2 includes a confidence interval. If you use the P-value method or the critical value method from Part 1 of this section to test the claim that women and men have the same mean hemoglobin levels, will the hypothesis tests and the confidence interval result in the same conclusion?

b. In general, if you conduct a hypothesis test using the methods of Part 1 of this section, will the P-value method, the critical value method, and the confidence interval method result in the same conclusion?

c. Assume that you want to use a 0.01 significance level to test the claim that the mean haemoglobin level in women is lessthan the mean hemoglobin level in men. What confidence level should be used if you want to test that claim using a confidence interval?

Short Answer

Expert verified

a. Yes, the hypothesis tests and the confidence interval results in the same conclusion.

b. Yes. The \(p\)-value method, the critical value method, and the confidence interval method result in the same conclusion.

c. \(98\% \)Confidence level should be used.

Step by step solution

01

Define inferential tests

a. Refer to exercise 2 for the claim that mean haemoglobin level in men and women is same.

The test is two-tailed.

The p-value method or critical value method pertaining to the claim would provide the same results for the test at the same level of significance. Further, the results derived from any of the two methods of hypothesis tests would be the same as the result derived from the confidence level at any corresponding level of confidence.

02

Compare the methods used in hypothesis tests and confidence intervals

b. The P-value method of hypothesis testing, the critical value method of hypothesis testing, along with confidence intervals all use the same distribution and standard error to derive results.

Thus, the results are expected to be equivalent in the sense that they result in the same conclusions.

03

Find the confidence level

c. It is desired to test the claim that the mean hemoglobin level in women is less than the mean hemoglobin level in men. The claim suggests a one-tailed hypothesis at a 0.01 level of significance.

Referring to 8-1, it can hence be concluded that the confidence level that is appropriate to test the claim is 98%.

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Most popular questions from this chapter

In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of\({n_1} - 1\)and\({n_2} - 1\).) Bad Stuff in Children’s Movies Data Set 11 “Alcohol and Tobacco in Movies” in Appendix B includes lengths of times (seconds) of tobacco use shown in animated children’s movies. For the Disney movies, n = 33,\(\bar x\)= 61.6 sec, s = 118.8 sec. For the other movies, n = 17,\(\bar x\)= 49.3 sec, s = 69.3 sec. The sorted times for the non-Disney movies are listed below.

a. Use a 0.05 significance level to test the claim that Disney animated children’s movies and other animated children’s movies have the same mean time showing tobacco use.

b. Construct a confidence interval appropriate for the hypothesis test in part (a).

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0 0 0 0 0 0 1 5 6 17 24 55 91 117 155 162 205

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Are Male Professors and Female Professors Rated Differently?

a. Use a 0.05 significance level to test the claim that two samples of course evaluation scores are from populations with the same mean. Use these summary statistics: Female professors:

n = 40, \(\bar x\)= 3.79, s = 0.51; male professors: n = 53, \(\bar x\) = 4.01, s = 0.53. (Using the raw data in Data Set 17 “Course Evaluations” will yield different results.)

b. Using the summary statistics given in part (a), construct a 95% confidence interval estimate of the difference between the mean course evaluations score for female professors and male professors.

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Do the larger samples in this exercise affect the results much?

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a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

c. If the significance level is changed to 0.01, does the conclusion change?

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a. Use a hypothesis test.

b. Use an appropriate confidence interval.

c. Does nausea appear to be an adverse reaction resulting from OxyContin?
See all solutions

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