Question

A sample of n = 29 reports a variance of 22.7. At the 10 % level does this indicate a population variance is less than 37.2? 1. True 2. False

Answer 1

let us state the hypothesis we need to test:

Under the null hypothesis,

where, T is the test statistic for testing this hypothesis.

T is defined as,

= population variance under the null hypothesis.

From our sample, we have, n=29,s²=22.7, =37.2, T=17.08602

We need to test this at level of significance.

P-value= P[ T < 17.08602 | H₀] = 0.05312966, which is less that 0.1

So, we reject the null hypothesis at 10% level.

so, At the 10 % level ,this indicates a population variance is less than 37.2.

Answer: True