Chapter 9: Q.11.46 (page 460)
A sample size that will ensure a margin of error of at most the one specified.
The required sample size is 6, 766
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Interpreting Displays.
In Exercises 5 and 6, use the results from the given displays.
Testing Laboratory Gloves, The New York Times published an article about a study by Professor Denise Korniewicz, and Johns Hopkins researched subjected laboratory gloves to stress. Among 240 vinyl gloves, 63% leaked viruses; among 240 latex gloves, 7% leaked viruses. See the accompanying display of the Statdisk results. Using a 0.01 significance level, test the claim that vinyl gloves have a greater virus leak rate than latex gloves.
Testing Claims About Proportions. In Exercises 7–22, 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.
Dreaming in Black and White A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 306 people over the age of 55, 68 dream in black and white, and among 298 people under the age of 25, 13 dream in black and white (based on data from “Do We Dream in Color?” by Eva Murzyn, Consciousness and Cognition, Vol. 17, No. 4). We want to use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. An explanation given for the results is that those over the age of 55 grew up exposed to media that was mostly displayed in black and white. Can the results from parts (a) and (b) be used to verify that explanation?
Repeat Exercise 12 “IQ and Lead” by assuming that the two population standard deviations are equal, so \({\sigma _1} = {\sigma _2}\). Use the appropriate method from Part 2 of this section. Does pooling the standard deviations yield results showing greater significance?
Degrees of Freedom
For Example 1 on page 431, we used df smaller of and , we got , and the corresponding critical values are If we calculate df using Formula 9-1, we get, and the corresponding critical values are . How is using the critical values of more “conservative” than using the critical values of .
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 \({p_1} = {p_2}\) (with a 0.05 significance level) and a 95% confidence interval estimate of \({p_1} - {p_2}\).
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