1) A researcher wishes to see if there is a difference in the manual dexterity of athletes and that of band members. Two random samples of 30 are selected from each group and are given a manual dexterity test. The mean of the athletes’ test was 87, and the mean of the band members’ test was 92. The population standard deviation for the test is 7.2. At \(\alpha= 0.01\), is there a significant difference in the mean scores?

2) The mean travel time to work for Americans is 25.3 minutes. An employment agency wanted to test the mean commuting times for college graduates and those with only some college. Thirty college graduates spent a mean time of minutes commuting to work with a population variance of 69.36. Thirty-nine workers who had completed some college had a mean commuting time of 36.94 minutes with a population variance of 35.01. At the 0.05 level of significance, can a difference in means be concluded? Use \(\mu_1\) for the mean for college graduates.

3) Two random samples of 32 individuals were selected. One sample participated in an activity which simulates hard work. The average breath rate of these individuals was 21 breaths per minute. The other sample did some normal walking. The mean breath rate of these individuals was 14. From a previous study we can conclude the population standard deviation of the hard work group is 5.4 and the population standard deviation for the normal group 7.2. Can it be concluded at a significance of 0.10 that there are more breaths per minute for the hard work group?