Question-71

Suppose \(X\) is normally distributed with unknown standard deviation \(\sigma\). Let \(X_1, X_2,\ldots,\) \(X_{16}\) be an i.i.d. sample with distribution \(X\) and a sample standard deviation \(s_X = 3.5\). What conclusion would a \(\chi^2\)-test reach if the null hypothesis assumes \(\sigma = 3\), with an alternate hypothesis that \(\sigma > 3\), and a significance level of \(\alpha = 0.05\)?

• Reject the null hypothesis.

• Do not reject the null hypothesis.

Hint

Answer

• Reject the null hypothesis.

• Do not reject the null hypothesis.

Solution