Question

Use the following null and alternative hypotheses to answer the following. Ho: LaTeX: \sigma^2=100 ? 2 = 100 Ha: LaTeX: \sigma^2\ne100 ? 2 ? 100 If n = 17, s = 6 and LaTeX: \alpha=0.05 ? = 0.05 state the decision. Since our test statistic is not in the rejection region, we reject the null hypothesis. Since our test statistic is in the rejection region, we reject the null hypothesis. Since our test statistic is in the rejection region, we do not reject the null hypothesis. Since our test statistic is not in the rejection region, we do not reject the null hypothesis.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis H₀: ?² = 100

Alternative hypothesis H_A: ?² 100

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data. Using sample data, the degrees of freedom (DF), and the test statistic (X²).

DF = n - 1 = 17 -1

D.F = 16

We use the Chi-Square Distribution Calculator to find P(?² > 44.44) = less than 0.001

Interpret results. Since the P-value (almost 0) is less than the significance level (0.05), we have to reject the null hypothesis.

Since our test statistic is in the rejection region, we reject the null hypothesis?.