Reference no: EM132964834

Consider the following competing hypotheses and relevant summary statistics:

HA: σ21/σ22 ≠ 1

H0: σ21/σ22 = 1

Sample 1: x¯ 1 = 49.9, s21 = 24.9, and n1 = 7

Sample 2: x¯ 2 = 54.0, s22 = 13.2, and n2 = 5

Assume that the two populations are normally distributed. (You may find it useful to reference the appropriate table: chi-square table or F table)

a. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Test statistic _________________

b. Find the p-value.

0.01 p-value < 0.025

0.05 p-value < 0.10

0.025 p-value < 0.05

p-value < 0.01

p-value 0.10

c. Do you reject the null hypothesis at the 5% significance level?

Yes, since the p-value is more than significance level.

No, since the p-value is more than significance level.

Yes, since the p-value is less than significance level.

No, since the p-value is less than significance level.

d. Interpret the results at α = 0.05.

We conclude that the population variances differ.

We cannot conclude that the population variances differ.

We conclude that population variance1 is greater than population proportion 2.

We cannot conclude that population variance 1 is greater than population variance 2.