Question

1. A UCLA researcher claims that the average life span of mice can be extended by as much as 8 months when the calories in their diet are reduced by approximately 40% from the time they are weaned. The restricted diets are enriched to normal levels by vitamins and protein. Suppose that a random sample of 10 mice is fed a normal diet and has an average life span of 32.1 months with a standard deviation of 3.2 months, while a random sample of 15 mice is fed the restricted diet and has an average life span of 37.6 months with a standard deviation of 2.8 months. Assume the distributions of life spans for the regular and restricted diets are approximately normal.

1. Test if the population variances are not equal at alpha 0.05.
2. Test the hypothesis, at the 0.05 level of significance, that the average life span of mice on this restricted diet is increased by 8 months against the alternative that the increase is less than 8 months.

Answer 1

Solution:

Hypotheses: Hou - Hz = 8 vs. H: H1-H2 < 3 Critical Region: SL: a = 0.05 df = net n -2= 10 + 15 - 2 = 23 to...(23)<-1.714 Test Statistic: First we need to calculate the pooled SD. (9)* 3.2+(14)* 2.82 -= 2.963 ==-2.05 Tawa *2- *, - H1-H2 5.5-8 2.963, 1015 Conclusion: Since Tobs <to.cs(23) we reject the null hypothesis and conclude that H.-Hz < 8 months.