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Chapter 9: Q3BSC (page 414)
Units of MeasureIf the values listed in Exercise 2 are changed so that they are expressed in Celsius degrees instead of Fahrenheit degrees, how are hypothesis test results affected?
Hypothesis test results are not affected by a change in the unit of measurement.
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Equivalence of Hypothesis Test and Confidence Interval Two different simple random samples are drawn from two different populations. The first sample consists of 20 people with 10 having a common attribute. The second sample consists of 2000 people with 1404 of them having the same common attribute. Compare the results from a hypothesis test of (with a 0.05 significance level) and a 95% confidence interval estimate of.
A sample size that will ensure a margin of error of at most the one specified.
In Exercises 5鈥�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 鈥淭able鈥� answers based on Table A-3 with df equal to the smaller of\({n_1} - 1\)and\({n_2} - 1\).)Blanking Out on Tests Many students have had the unpleasant experience of panicking on a test because the first question was exceptionally difficult. The arrangement of test items was studied for its effect on anxiety. The following scores are measures of 鈥渄ebilitating test anxiety,鈥� which most of us call panic or blanking out (based on data from 鈥淚tem Arrangement, Cognitive Entry Characteristics, Sex and Test Anxiety as Predictors of Achievement in Examination Performance,鈥� by Klimko, Journal of Experimental Education, Vol. 52, No. 4.) Is there sufficient evidence to support the claim that the two populations of scores have different means? Is there sufficient evidence to support the claim that the arrangement of the test items has an effect on the score? Is the conclusion affected by whether the significance level is 0.05 or 0.01?
Questions Arranged from Easy to Difficult | ||||
24.64 | 39.29 | 16.32 | 32.83 | 28.02 |
33.31 | 20.60 | 21.13 | 26.69 | 28.9 |
26.43 | 24.23 | 7.10 | 32.86 | 21.06 |
28.89 | 28.71 | 31.73 | 30.02 | 21.96 |
25.49 | 38.81 | 27.85 | 30.29 | 30.72 |
Questions Arranged from Difficult to Easy | |||
33.62 | 34.02 | 26.63 | 30.26 |
35.91 | 26.68 | 29.49 | 35.32 |
27.24 | 32.34 | 29.34 | 33.53 |
27.62 | 42.91 | 30.20 | 32.54 |
Testing Claims About Proportions. In Exercises 7鈥�22, 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.
Cell Phones and Handedness A study was conducted to investigate the association between cell phone use and hemispheric brain dominance. Among 216 subjects who prefer to use their left ear for cell phones, 166 were right-handed. Among 452 subjects who prefer to use their right ear for cell phones, 436 were right-handed (based on data from 鈥淗emi- spheric Dominance and Cell Phone Use,鈥� by Seidman et al., JAMA Otolaryngology鈥擧ead & Neck Surgery, Vol. 139, No. 5). We want to use a 0.01 significance level to test the claim that the rate of right-handedness for those who prefer to use their left ear for cell phones is less than the rate of right-handedness for those who prefer to use their right ear for cell phones. (Try not to get too confused here.)
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
Verifying requirements in the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group considered of 201,229 children given the sulk vaccine for polio, and 33 of those children developed polio. The other 200,745 children were given a placebo, and 115 of those children developed polio. If we want to use the methods of this section to test the claim that the rate of polio is less for children given the sulk vaccine, are the requirements for a hypothesis test satisfied? Explain.
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