5. Independent random samples were taken from populations of histidine (an amino acid) levels for males and females. The data from the two samples are given below. Assuming equal population variances, at the 0.10 level of significance test if the histidine levels for the two groups are the same.

Population 1: Males n₁ = 5 X₁ =300.8 S₁² = 15,291.7

Population 2: Females n₂ = 10 X₂ =153.2 S₂² = 2,484.62

6. A trucking firm is considering the installation of a new engine air filter for its long-haul trucks, but does not want to make the switch unless the new filter can be shown to enhance the fuel economy (in terms of greater miles per gallon) of these vehicles. A test is set up in which each truck makes the same run twice: once with the current filtration system and once with the new. Given the sample results shown below, test at the 0.05 significance level to evaluate whether the firm should switch to the new filtration system.

Truck # Current Filter (mpg) New Filter (mpg)

1 8 7

2 5 7

3 10 8

4 7 10

5 6 9

6 5 6

7 6 8

8 7 7

7. Medical researchers monitoring two groups of people over a six-year period found that of 3,429 people who took aspirin daily, 148 died from a heart attack. During the same period, of 1,710 people who received a placebo instead of aspirin, 79 died from the same cause. At the 0.10 significance level, determine whether taking a placebo is as effective as taking aspirin in reducing the likelihood of a heart attack.

8. A sample of 9 technicians exposed to the standard version of a training film required an average of 31.4 minutes to service a compressor system, with a standard deviation of 14.5 minutes. For 7 technicians viewing an alternative version of the film, the average time required was 22.3 minutes, with a standard deviation of 10.2 minutes.

If the sampled populations are approximately normally distributed, can the population standard deviations be assumed to be equal? Test at the 0.05 significance level.

9. In two independent samples from populations that are normally distributed, X_{A =}165.0, S_A = 21.5, and n_A = 40 and X_B = 172.9, S_B = 31.3, and n_B = 32. Use = 0.02 to test whether the population standard deviations can be assumed to be equal.