Testing: H 1 : χ 2 ≠ 7.46 Your sample consists of 41 subjects, with a variance of 2.48. Calculate the test statistic, rounded to 2 decimal places. χ 2 =

Answer 1

Hi Jenny!

It seems like probably this is intended to be a hypothesis test about whether a given variance is detected to be different from 7.46. You would write the hypotheses like this:

H₀: σ² = 7.46

H₁: σ² ≠ 7.46

The next step is to find the test statistic, which is X² = (n-1)s²/σ². Under the null hypothesis, X² is distributed χ²_n-1.

For this case, X² = (41-1) * 2.48 / 7.46.

In this case, rounded to two decimal places that turns out to be 13.30.

The next part of the problem is to look up critical value(s) from the Chi-Square distribution with 40 degrees of freedom. For a two-sided test, the acceptance region is between 24.43 and 59.34 for a 0.05-size test. This means you would reject H₀ if X² is less than 24.43 or greater than 59.34. Therefore for this test, you'll reject H₀ and find that you have strong evidence to believe σ² ≠ 7.46!