Stats

Math 321 – Reading Assignment – Chapters 9-11 You are to identify the problem type for each of the 9 problems. You do not need to check any conditions, just list the basic type of the test is a problem involves a hypothesis test. Here are the 9 potential types of problems we have covered.

• Chapter 9 o Confidence Interval for a Proportion o Sample Size for a Proportion o Confidence Interval for a Mean o Sample Size for a Mean

• Chapter 10 o One-Proportion Test o One-Mean Test

• Chapter 11 o Two-Proportion Test o Paired Difference Test o Two-Mean Test

To receive full credit, you must list which wording and information you used to make your decision. 1) A nutritionist has developed a diet that she claims will help people lose weight. Twelve people were randomly selected to try the diet. Their weights were recorded prior to beginning the diet and again after 6 months. Here are the original weights, in pounds, with the weight after 6 months in parentheses.

Before 192 212 171 215 180 207 165 168 190 184 200 196 After 183 196 174 211 160 191 162 175 190 179 189 195

Test the claim that the diet is effective at the 0.05 level of significance. 2) A sample of 100 male drivers showed an annual mean of 10230 miles driven per year, with a standard deviation of 2870 miles. A similar sample of 28 female drivers showed an annual mean of 9660 miles driven per year, with a standard deviation of 2900 miles. Test the claim that the mean number of miles driven by male drivers is greater than the mean number of miles driven per year by female drivers at the 0.05 level of significance.

3) A researcher wants to determine what percent of high school students have asthma. How large of a sample does she need in order to be 95% confident that her estimate is within 6% of the true percentage of all high school students with asthma? 4) What proportion of all drivers turn on their headlights while driving in the rain? A sample of 200 vehicles on a rainy day showed that 41 had their headlights turned on. Test the claim that less than 25% of all drivers turn on their headlights while driving in the rain at the 0.01 level of significance. 5) A researcher wants to estimate the mean height of college-aged men. A sample of 50 college-aged men had a mean height of 70.6 inches and a standard deviation of 2.3 inches. Construct a 95% confidence interval for the mean height of all college-aged men. 6) A sample of 38 60-year-old smokers revealed that 10 of them have suffered with some sort of heart disease. A sample of 162 60-year-old nonsmokers showed that 12 of them have suffered with some sort of heart disease. At the 0.01 level of significance, test the claim that nonsmokers are less likely to suffer with some sort of heart disease by the time they turn 60 years old.

7) A researcher wants to estimate the mean student loan debt for students who graduate from a 4-year public university. How large of a sample does the researcher need to take in order to be 90% confident that the estimate is within $1000 of the mean debt for all graduates of a 4-year public university. Use a standard deviation of $8000. 8) A research team decides to estimate the percentage of college students who are married. A random sample of 2500 college student revealed that 175 of them were married. Construct a 95% confidence interval for the proportion of all college students who are married. 9) UPS monitors its trainees to see how fast they can work. A sample of 20 new employees handled a mean of 460.4 packages in one day, with a standard deviation of 38.83 packages. Test the claim that the mean number of packages handled per day by new employees is more than 450 packages, using the 0.05 level of significance.