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Comparing graphs of the standard normal distribution z-distribution and a t-distribution with 15 degrees of freedom df , how are they similar? Use the following information to answer the next five exercises. Body temperature is known to be distributed normally among healthy adults. Because you do not know the population standard deviation, you use the t-distribution to study body temperature. You collect data from a random sample of 20 healthy adults and find that your sample temperatures have a mean of What is the degrees of freedom df for this study? Round to two decimal places. Suppose your sample size had been 30 rather than Round to two decimal places 8. You conduct a poll of randomly selected city residents, asking them if they own an automobile.
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Write the null and alternative hypotheses to test this. If you reject H0 when H0 is correct, what type of error is this? If you fail to reject H0 when H0 is false, what type of error is this? What is the relationship between the Type II error and the power of a test? A new blood test is being developed to screen patients for cancer. Positive results are followed up by a more accurate and expensive test. It is assumed that the patient does not have cancer.
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Describe the null hypothesis, the Type I and Type II errors for this situation, and explain which type of error is more serious. The null hypothesis is that the patient does not have TB. Explain in words what it means that a screening test for TB has a power of 0. If you are conducting a hypothesis test of a single population mean, and you do not know the population variance, what test will you use if the sample size is 10 and the population is normal? If you are conducting a hypothesis test of a single population mean, and you know the population variance, what test will you use? If you are conducting a hypothesis test of a single population proportion, with np and nq greater than or equal to five, what test will you use, and with what parameters?
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Published information indicates that, on average, college students spend less than 20 hours studying per week. You draw a sample of 25 students from your college, and find the sample mean to be What distribution will you use to test whether study habits at your college are the same as the national average, and why? A published study says that 95 percent of American children are vaccinated against measles, with a standard deviation of 1. You draw a sample of children from your community and check their vaccination records, to see if the vaccination rate in your community is the same as the national average.
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What distribution will you use for this test, and why? If you get a result with a p-value of 0. You believe children with a particular disease are smaller than average, so you draw a sample of 20 children with this disease and find a mean height of What are the null and alternative hypotheses for this study? What distribution will you use to test your hypothesis, and why? What is the test statistic and the p-value? Based on your sample results, what is your decision? Suppose the mean for your sample was Redo the calculations and describe what your decision would be. What is the level of significance for this study? Nationally, 80 percent of adults own an automobile. You are interested in whether the same proportion in your community own cars.
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You draw a sample of and find that 75 percent own cars. What test will you use, and why? You conduct a poll of political opinions, interviewing both members of 50 married couples. Are the groups in this study independent or matched? You are testing a new drug to treat insomnia. You randomly assign 80 volunteer subjects to either the experimental new drug or control standard treatment conditions. You are investigating the effectiveness of a new math textbook for high school students. Use the following information to answer the next two exercises. You are conducting a study of the difference in time at two colleges for undergraduate degree completion. At College A, students take an average of 4. The pooled standard deviation for this data is 1. Suppose the mean time to earn an undergraduate degree at College A was 5.
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Calculate the effect size and interpret it. You conduct an independent-samples t-test with sample size ten in each of two groups. College students in the sciences often complain that they must spend more on textbooks each semester than students in the humanities. To test this, you draw random samples of 50 science and 50 humanities students from your college, and record how much each spent last semester on textbooks. Consider the science students to be group one, and the humanities students to be group two. What is the random variable for this study? Use an alpha level of 0. What is your conclusion? You want to know if proportion of homes with cable television service differs between Community A and Community B.
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To test this, you draw a random sample of for each and record whether they have cable service. What are the null and alternative hypotheses for this study If 65 households in Community A have cable service, and 78 households in community B, what is the pooled proportion?
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