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Soc 5811: Practice Problem Set- Confidence Intervals and Hypothesis Testing 1. A researcher is interested in whether or not high school students are passing a new statewide exit exam. A random sample of 100 students has a mean of 76 and a standard deviation of 15. Calculate and draw the 95% confidence interval around the mean. Can we be confident that the population mean is above a passing grade of 70? 2. A drug company wants to know if its new drug lowers cholesterol below the target level of 120. A random sample of 25 patients has a mean of 115 and a standard deviation of 20. Calculate and draw a 99% confidence interval around the mean. Can we be confident that the population mean is below 120? Recalculate and redraw a 90% confidence interval around the mean. Can we be confident at this level? 3. Determine the 95% confidence interval for a sample with the following properties: N=36, Ybar=132, s=24. Draw the sampling distribution around a population mean of 120. Does the population mean fall inside or outside the confidence interval? 4. Test the null hypothesis that μ=40 using a random sample of 1000 cases with a Y-bar=45 and an s=16. Use a two-tailed test with an alpha=.05. Draw the sampling distribution around the mean and label where your test statistic falls in relation to the mean. 5. Test the null hypothesis that μ=100 using a random sample of 49 cases with a Y-bar=96 and an s=16. Use a one-tailed test with an alpha=.01. Draw the sampling distribution around the mean and label where your test statistic falls in relation to the mean. Use your test-statistic to estimate the probability of drawing this sample, or one larger, if μ=100. 6. A toothpaste company wants to know if its new product increases the length of time in between dentist visits for its users. The company sets a target of 180 days to determine if its product prevents dentist visits longer than other toothpastes. A random sample of 49 customers is taken with a mean of 186 days and a standard deviation of 20. Set up a one-tailed test with an alpha=.05. Draw the sampling distribution around the mean and label where your test statistic falls in relation to the mean. Can the toothpaste company be confident that its new product lengthens time between visits? 7. Determine whether or not the mean household income in Minnesota and Iowa are the same. A random sample of 50 Minnesotans has a Y-bar=$52,000 and an s=1,200. A random sample of 50 Iowans has a Y-bar=$47,000 and an s=1,400. Use a two-tailed test with an alpha=.05. Draw the sampling distribution for the difference in means and label where your test statistic falls in relation to the mean. Can we reject the null hypothesis? 8. Compare the mean, variance, and standard deviation for the following two groups: Group 1: 61, 64, 64, 67, 69, 70, 71, 71, 72, 75, 80, 83, 84 Group 2: 62, 63, 65, 65, 68, 69, 70, 74, 78, 79, 80, 82, 90 Test the null hypothesis that means of the two groups are equal. Use a two-tailed test with an alpha-level of .05.