Chapter 7 HW Handout #2: Complete the four problems below using the procedures on the Confidence Interval Flow Chart. Show ALL work.

  1. A dietitian has developed a diet that is low in fats, carbohydrates, and cholesterol. Although the diet was intended to be used by people with heart disease, the dietitian wishes to examine the effect this diet has on the weights of obese people. Two random samples of 100 obese people each are selected, and one group of 100 is placed on the low-fat diet. The other 100 are placed on a diet that contains approximately the same quantity of food but is not low in fats, carbohydrates, and cholesterol. For each person, the amount of weight lost (or gained) in a 3-week period is recorded. The summary statistics are shown in the table below.
    DietNMeanSD
    Low fat1009.314.67
    Regular1007.404.04
    1. Create a 95% confidence interval for the difference between the population mean weight losses for the two diets.
    2. Interpret your confidence interval.
    3. Does this confidence interval suggest that obese people will lose more weight on a low-fat diet? Explain.
  2. A Statistics student designed an experiment to see if there was any real difference in battery life between brand-name AA batteries and generic AA batteries. He used six pairs of AA alkaline batteries from two major battery manufacturers: a well known brand name and a generic brand. He measured the length of battery life while playing a CD continuously. He recorded the time in minutes until the sound stopped. A summary of the results is shown below.
    BatteryNMeanSD
    Generic6206.010.3
    Brand-name6187.414.6
    1. Create a 95% confidence interval for the difference between the population mean battery life of the two types of AA batteries.
    2. Interpret your confidence interval.
    3. Does this confidence interval suggest that generic AA batteries will last longer than brand-name AA batteries? Explain.
  3. The Centers for Disease Control report a survey of randomly selected Americans age 65 and older, which found that 405 of 1006 men and 530 of 1057 women suffered from some form of arthritis.
    1. Create a 95% confidence interval for the difference in the proportions of senior men and women who have the disease.
    2. Interpret your confidence interval.
    3. Does this confidence interval suggest that arthritis is more likely to afflict women than men? Explain.
  4. In October 2000, the U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 85% of the 12,460 males and 88% of the 12675 females indicated that they had high school diplomas.
    1. Create a 90% confidence interval for the difference in graduation rates between males and females.
    2. Interpret your confidence interval.
    3. Does this provide strong evidence that girls are more likely than boys to complete high school? Explain.