Perform the required chi-square hypothesis test. Preliminary data analyses and other information indicate that it isreasonable to assume that the variable under consideration is normally distributed. Use the critical-value approach or theP-value approach as indicated.
-The standard deviation of math test scores at one high school is 16.1. The standard deviation of the math scores of a random sample of 22 girls was 12. Use a significance level of 0.01 to test whether the standard deviation, Ϭ, of the girls' test scores is smaller than 16.1. Use the critical-value approach.

Question

Quizplus · Accepted Answer

The Answer is

\begin{array} { l } \mathrm { H } _ { 0 } : \sigma = 16.1 \quad \mathrm { H } _ { \mathrm { a } } : \sigma < 16.1 \ \alpha = 0.01 \end{array}

Test statistic:

X ^ { 2 } = 11.666

. Critical value

= 8.897

. Do not reject

\mathrm { H } _ { 0 }

. At the

1 \%

level of significance, the data do not provide sufficient evidence to conclude that the standard deviation of the girls' test scores is smaller than 16.1.

Perform the Required Chi-Square Hypothesis Test