Question

Random samples of sizes n1 = 25 and n2 = 20 were selected from populations A and B, respectively. From the samples, the standard deviations were computed to be s1 = 5.2 and s2 = 6.8.
a. Do the data provide substantial evidence to indicate the populations have different standard deviations? Use α = .05.
b. Estimate the relative sizes of the standard deviations by constructing a 95% confidence interval for the ratio of the standard deviations σ1/σ2.
c. The data and populations must satisfy what conditions in order for your test and confidence interval to be valid?

Answer 1

1 = 25, n2 = 20, s1 = 5.2, s2 = 6.8 n1 =15, n2 = 10, df1 = 14, df2 = 9, s1 = 5.3, s2 = 8.8

 

a. H0: σ1 = σ2 versus Ha: σ1 ≠ σ2

With α = 0.05, reject H0:

Thus, we fail to reject H0 and conclude there is not sufficient evidence that there is a difference in the two standard deviations.

 

b.

 

c.         We need to assume that the two samples were independent random samples from normally distributed populations.

c.         We need to assume that the two samples were independent random samples from normally distributed populations.