Exercises - Comparing Means

  1. Listed below are times (seconds) that animated Disney movies showed the use of tobacco and alcohol. Use a 0.05 significance level to test the claim that the mean of the differences is greater that 0 seconds, so that more time is devoted to showing tobacco than alcohol. Use the critical value method. $$\begin{array}{l|cccccccccc} \textrm{Tobacco} & 176 & 51 & 0 & 299 & 74 & 2 & 23 & 205 & 6 & 155\\\hline \textrm{Alcohol} & 88 & 33 & 113 & 51 & 0 & 3 & 46 & 73 & 5 & 74\\ \end{array}$$

  2. Many studies have been conducted to test the effects of marijuana use on mental abilities. In one such study, groups of light and heavy users of marijuana in college were tested for memory recall, with the results given below.

    $$\begin{array}{ccc} \textrm{Items sorted correctly by light marijuana users} & & \textrm{Items sorted correctly by heavy marijuana users}\\ n = 64,\, \overline{x} = 53.3,\, s = 3.6 & & n = 65,\, \overline{x} = 51.3,\, s = 4.5 \end{array}$$
    1. Use the P-value method with a 0.01 significance level to test the claim that the population of heavy marijuana users has a lower mean than the light users.

    2. Construct a 98% confidence interval for the difference between the two population means. What does the confidence interval suggest about the equality of the two population means?

  3. A researcher suggests that male nurses earn more than female nurses. A survey of 16 male nurses and 20 female nurses reports these data. Assume the distributions are normal and use $\alpha = 0.05$. $$\begin{array}{cc} \textrm{Female} & & \textrm{Male}\\ n = 20,\, \overline{x} = \$23570,\, s = \$250 & & n = 16,\, \overline{x} = \$23800,\, s = \$300 \end{array}$$

    1. Are the variances equal?

    2. Test the claim that male nurses earn more than female nurses.