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Problem 1 Suppose 40% of registered voters in a certain town are Democrats. You take a simple random sample of 80 voters. a) If your survey avoids biases, you expect __________ Democrats, give or take ____________ or so, in your sample. b) What is the probability that your sample actually predicts a Republican victory? Problem 2 A student doing a survey at a large university found that her random sample of 160 students reported an average GPA of 3.5 with a standard deviation of 0.45. The registrar’s office published the average GPA to be 2.85. Can the difference be explained by sampling variability? If not, how else can it be explained? Problem 3 A simple random sample of size n =70 has a mean of 87 and a sample SD of 0.5. a) Find a 98% confidence interval for the population mean. b) How important is it that we don’t know the shape of the population? Problem 4 The Motor Vehicle Department plans to estimate the proportion of drivers who have not received any tickets for moving violations during the past three years. How large a sample of its records should it take to be within 0.02 of the true proportion with 99% confidence? Problem 5 Consider the following matched-pair data set. Assume normality of the parent populations. Find a 95% confidence interval for the difference in means. x: 7 9 9 6 8 8 y: 4 4 3 4 9 5 Problem 6 To determine the effectiveness of a certain vitamin supplement, the weight increase for two groups of mice was measured: Control group: 12 Treatment group: 18 19 16 14 23 20 23 Test at the 5% level of significance whether the vitamins treatment results in a higher weight gain.