Suppose I surveyed a random sample of commuters who had jobs in Manhattan, 51 whose primary mode of transportation was bus (B) or subway (S) and 80 whose primary mode was Metro-North (MN) or the Long Island Railroad (LIRR).  Of the 51 in the first group, the mean annual income was $40,000 with a standard deviation of $5,100; of the 80 in th

For a study conducted by the research department of a pharmaceutical company, 245 randomly selected individuals were asked to report the amount of money they spend annually on prescription allergy relief medication. The sample mean was found to be $17.80 with a standard deviation of $4.30. A random sample of 225 individuals was selected independently of the first sample. These individuals reported their annual spending on non-prescription allergy relief medication. The mean of the second sample was found to be $18.20 with a standard deviation of $3.60. As the sample sizes were quite large, it was assumed that the respective population standard deviations of the spending for prescription and non-prescription allergy relief medication could be estimated as the respective sample standard deviation values given above. Construct a 90% confidence interval for the difference H₁ H₂ between the mean spending on prescription allergy relief medication (₁) and the mean spending on non-prescription…

3. An extensive study of the cost of health care in the United States presented data showing that the mean spending per Medicare enrollee in 2003 was $6883 (Monday, Fall 2003). To investigate differences across the country, a researcher took a sample of 49 Medicare enrollees in Indianapoli with a mean spending of $5978.32 and a standard deviation is $2513.

In a large section of a statistics​ class, the points for the final exam are normally​ distributed, with a mean of 7676 and a standard deviation of 77. Grades are assigned such that the top​ 10% receive​ A's, the next​ 20% received​ B's, the middle​ 40% receive​ C's, the next​ 20% receive​ D's, and the bottom​ 10% receive​ F's. Find the lowest score on the final exam that would qualify a student for an​ A, a​ B, a​ C, and a D.