A researcher wishes to compare the incomes of men and women. She selects a random sample of 80 married women. She records the weekly income of each of these women. Using the husbands of these women as the sample of men, she also records the weekly income of each man. She obtains the following summary statistics. $$\begin{array} { r | r } \text { Women } & \text { Men } \ \hline \mathrm { x } _ { 1 } = 520 & \mathrm { x } _ { 2 } = 590 \ \mathrm {~s} _ { 1 } = 220 & \mathrm {~s} _ { 2 } = 240 \ \mathrm { n } _ { 1 } = 80 & \mathrm { n } _ { 2 } = 80 \end{array}$$ Incomes are known to be normally distributed for both populations (women and men). Furthermore, the two population standard deviations are known to be equal. Is it reasonable to use the pooled t-test on these data? Explain your answer.

Question

A researcher wishes to compare the incomes of men and women. She selects a random sample of 80 married women. She records the weekly income of each of these women. Using the husbands of these women as the sample of men, she also records the weekly income of each man. She obtains the following summary statistics. $$\begin{array} { r | r }  \text { Women } & \text { Men } \ \hline \mathrm { x } _ { 1 } = 520 & \mathrm { x } _ { 2 } = 590 \ \mathrm {~s} _ { 1 } = 220 & \mathrm {~s} _ { 2 } = 240 \ \mathrm { n } _ { 1 } = 80 & \mathrm { n } _ { 2 } = 80 \end{array}$$ Incomes are known to be normally distributed for both populations (women and men). Furthermore, the two population standard deviations are known to be equal. Is it reasonable to use the pooled t-test on these data? Explain your answer.

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The Answer of A researcher wishes to compare the incomes of men and women. She selects a random sample of 80 married women. She records the weekly income of each of these women. Using the husbands of these women as the sample of men, she also records the weekly income of each man. She obtains the following summary statistics. $$\begin{array} { r | r }  \text { Women } & \text { Men } \ \hline \mathrm { x } _ { 1 } = 520 & \mathrm { x } _ { 2 } = 590 \ \mathrm {~s} _ { 1 } = 220 & \mathrm {~s} _ { 2 } = 240 \ \mathrm { n } _ { 1 } = 80 & \mathrm { n } _ { 2 } = 80 \end{array}$$ Incomes are known to be normally distributed for both populations (women and men). Furthermore, the two population standard deviations are known to be equal. Is it reasonable to use the pooled t-test on these data? Explain your answer.

A Researcher Wishes to Compare the Incomes of Men and Women