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Chapter 11: Q 3. (page 716)
P-values For each of the following, find the value using Table Then
calculate a more precise value using technology.
a.
b.
Part (a) value
Part (b) value
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The National Longitudinal Study of Adolescent Health interviewed a random sample of teens (grades to ). One question asked, “What do you think are the chances you will be married in the next years?” Here is a two-way table of the responses by gender:
Which of the following is the appropriate null hypothesis for performing a chi-square test?
a. Equal proportions of female and male teenagers are almost certain they will be married in years.
b. There is no difference between the distributions of female and male teenagers’ opinions about marriage in this sample.
c. There is no difference between the distributions of female and male teenagers’ opinions about marriage in the population.
d. There is no association between gender and opinion about marriage in the sample.
e. There is no association between gender and opinion about marriage in the population.
Stress and heart attacks You read a newspaper article that describes a study of whether stress management can help reduce heart attacks. The subjects all had reduced blood flow to the heart and so were at risk of a heart attack. They were assigned at random to three groups. The article goes on to say:
One group took a four-month stress management program, another underwent a four-month exercise program, and the third received usual heart care from their personal physicians. In the next three years, only of the people in the stress management group suffered "cardiac events," defined as a fatal or non-fatal heart attack or a surgical procedure such as a bypass or angioplasty. In the same period, of the people in the exercise group and out of the patients in usual care suffered such events.
a. Use the information in the news article to make a two-way table that describes the study results.
b. Compare the success rates of the three treatments in preventing cardiac events.
c. Do the data provide convincing evidence at the level that the true success rates for patients like these are not the same for the three treatments?
Aw, nuts! A company claims that each batch of its deluxe mixed nuts
contains cashews, almonds, macadamia nuts, and 8% Brazil nuts. To test this claim, a quality-control inspector takes a random sample of nuts from the latest batch. The table displays the sample data.
a. State appropriate hypotheses for performing a test of the company’s claim.
b. Calculate the expected count for each type of nut.
c. Calculate the value of the chi-square test statistic.
For these data, with a P-value of approximately . Assuming that the researchers used a significance level of , which of the following is true?
a. A Type I error is possible.
b. A Type II error is possible.
c. Both a Type I and a Type II error are possible.
d. There is no chance of making a Type I or Type II error because the P-value is approximately .
e. There is no chance of making a Type I or Type II error because the calculations are correct.
A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race or ethnicity of the driver. The results are summarized in the following table.
The proportion of this city's population in each of the racial/ethnic categories listed is as follows.
We wish to test : The racial/ethnic distribution of traffic tickets in the city is the same as the racial/ethnic distribution of the city's population.
The category that contributes the largest component to the test statistic is a. White, with fewer tickets than expected.
b. White, with more tickets than expected.
c. Hispanic, with fewer tickets than expected.
d. Hispanic, with more tickets than expected.
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