Spring 2013Math 227Test #3Name: ______

Total: 100 points. For confidence interval, please write down the critical value(s) and margin of error (if needed), then write the confidence interval. For Hypothesis testing, use either the traditional method or the P-value method.

  1. (10)A survey found that 45% of a sample of 799 teens admitted to misrepresenting their age online to access websites and online service. Construct a 90% confidence interval for the percent of teens who have misrepresented their age online.
  1. (12)You have been hired by a college foundation to conduct a survey of graduates.
  2. If you want to estimate the percentage of graduates who have made a donation to the college after graduation, how many graduates must you survey if you want 98% confidence that your percentage has a margin of error of five percentage points?
  1. If you want to estimate the mean amount of all charitable contributions made by graduates, how many graduates must you survey if you want 98% confidence that your sample mean is in error by no more than $50? Based on results from a pilot study, assume that the standard deviation of donations by graduates is $337.
  1. (18)Consumer Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving (assume that this is a random sample selected from a normally distributed population):

13016015012012011017016011013090

a. Create a 95% confidence interval for the average calorie content of vanilla yogurt.

b. A diet guide claims that you will get an average of 120 calories from a serving of vanilla yogurt. At 5% significant level, test this claim.

  1. (10)The Centers for Disease Control and Prevention reported a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and 535 of 1062 women suffered from some form of arthritis. Create a 95% confidence interval for the difference in the proportions of senior men and women who have this disease. Does this confidence interval suggest that arthritis is more likely to afflict women than men? Explain.
  1. (10)Listed below are the costs (in dollars) of repairing the front ends and rear ends of different cars when they were damaged in controlled low-speed crash tests. Test a claim that the front repair costs are greater than the corresponding rear repair costs. Assume the values come from a normally distributed population.

Front repair cost / 936 / 978 / 2252 / 1032 / 3911 / 4312 / 3469 / 2598 / 4535
Rear repair cost / 1480 / 1202 / 802 / 3191 / 1122 / 739 / 2769 / 3375 / 1787
  1. (10)A simple random sample of 1862 births of Asian babies resulted in a mean birth weight of 3171 g and a standard deviation of 428 g. Use a 0.01 significance level to test the claim that the mean birth weight of Asian babies is less than the mean birth weight of 3369 g for Caucasian babies.
  1. (10)A drug manufacturer believes that the manufacturing process is in control if the standard deviation of the dosage in each tablet is at most 0.10 milligrams. Suppose a sample of 30 tablets is evaluated, and the sample standard deviation is found to be 0.14 milligram. At 0.01 significance level, test the claim that the manufacturing process is in control. Assume that the sample is selected from a normally distributed population.
  1. (10)In April 2009, the Gallup organization surveyed 676 adults aged 18 and older and found that 352 believed they would not have enough money to live comfortably in retirement. Does the sample evidence suggest that a majority of adults in the United States believe they will not have enough money in retirement? Use 0.05 level of significance.
  1. (10)In a Gallup poll conducted, 513 national adults aged 18 years of age or older who consider themselves to be Republican were asked, “Of every tax dollar that goes to the federal government in Washington, D.C., how many cents of each dollar would you say are wasted?” The mean wasted was found to be 54 cents with a standard deviation of 2.9 cents. The same question was asked of 513 national adults aged 18 years of age or older who consider themselves to be Democrat. The mean wasted was found to be 41 cents with a standard deviation of 2.6 cents. Construct a 95% confidence interval for the mean difference in government waste. What can you conclude?

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