Perform the required hypothesis test for two population standard deviations. Assume that independent samples havebeen randomly selected from the two populations and that the variable under consideration is normally distributed onboth populations. Use the critical-value approach.
-A researcher obtained independent random samples of men from two different towns. She recorded the weights of the men. The results are summarized below: $$\begin{array} { l l } \frac { \text { Town } \mathrm { A } } { \mathrm { n } _ { 1 } = 61 } & \frac { \text { Town } \mathrm { B } } { \mathrm { n } _ { 2 } = 31 } \ \overline { \mathrm { x } } _ { 1 } = 165.1 \mathrm { lb } & \overline { \mathrm { x } } _ { 2 } = 159.5 \mathrm { lb } \ \mathrm { s } = 26.4 \mathrm { lb } & \mathrm { s } = 25.6 \mathrm { lb } \end{array}$$ Do the data provide sufficient evidence to conclude that there is more variation in weights of men from town A than in weights of men from town B? Perform an F-test at the 1% significance level.

Question

Perform the required hypothesis test for two population standard deviations. Assume that independent samples havebeen randomly selected from the two populations and that the variable under consideration is normally distributed onboth populations. Use the critical-value approach.
-A researcher obtained independent random samples of men from two different towns. She recorded the weights of the men. The results are summarized below: $$\begin{array} { l l }  \frac { \text { Town } \mathrm { A } } { \mathrm { n } _ { 1 } = 61 } & \frac { \text { Town } \mathrm { B } } { \mathrm { n } _ { 2 } = 31 } \ \overline { \mathrm { x } } _ { 1 } = 165.1 \mathrm { lb } & \overline { \mathrm { x } } _ { 2 } = 159.5 \mathrm { lb } \ \mathrm { s } = 26.4 \mathrm { lb } & \mathrm { s } = 25.6 \mathrm { lb } \end{array}$$ Do the data provide sufficient evidence to conclude that there is more variation in weights of men from town A than in weights of men from town B? Perform an F-test at the 1% significance level.

Quizplus · Accepted Answer

The Answer is

\begin{array} { l } \mathrm { H } _ { 0 } : \sigma _ { 1 } = \sigma _ { 2 } . \quad \mathrm { H } _ { \mathrm { a } } : \sigma _ { 1 } > \sigma _ { 2 } \ \alpha = 0.01 \end{array}

Test statistic:

F = 1.06

. Critical value

= 2.21

. Do not reject the null hypothesis. At the

1 \%

significance level, the data do not provide sufficient evidence to conclude that there is more variation in weights of men from town A than in weights of men from town

B

.

Perform the Required Hypothesis Test for Two Population Standard Deviations