The researcher's null hypothesis is H₀: σ² ≤ 22. A sample of n = 25 items yields a sample variance of s² = 28.5. The critical value of chi-square for a right-tailed test at α = .05 is: A)1.960 B)1.645 C)13.85 D)36.42

Question

Quizplus · Accepted Answer

To find the critical value of chi-square, we need to use the formula:

χ^2 = (n-1) * s^2 / σ^2

where n is the sample size, s^2 is the sample variance, and σ^2 is the hypothesized population variance.

Substituting the given values, we get:

χ^2 = (25-1) * 28.5 / 22 ≤ 31.4068

To find the critical value of chi-square for a right-tailed test at α = .05, we need to look up the value in the chi-square distribution table with (25-1) degrees of freedom and a probability of 0.95 (1-α). The closest value is 36.42, which corresponds to a probability of 0.95.

Therefore, the best choice is D, 36.42, because it is the critical value of chi-square for a right-tailed test at α = .05 with (25-1) degrees of freedom.

The Researcher's Null Hypothesis Is H0: σ2 ≤ 22

The Researcher's Null Hypothesis Is H₀: σ² ≤ 22