Suppose a researcher wants to perform a hypothesis test to compare the mean systolic blood pressure for men with the mean systolic blood pressure for women, based on independent samples. She obtains a random sample of 30 married couples and determines the mean systolic blood pressure for the men, $\bar { x } _ { 1 }$, and the mean systolic blood pressure for the women, $\bar { x } _ { 2 }$. She formulates the hypotheses as follows $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$ $\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } \neq \mu _ { 2 }$ and will reject the null hypothesis if $\bar { x } _ { 1 } - \bar { x } _ { 2 }$, the observed difference between the sample means is too large. She will use a two-means z-test. Identify the flaw in her methodology.

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The Answer of Suppose a researcher wants to perform a hypothesis test to compare the mean systolic blood pressure for men with the mean systolic blood pressure for women, based on independent samples. She obtains a random sample of 30 married couples and determines the mean systolic blood pressure for the men, $\bar { x } _ { 1 }$, and the mean systolic blood pressure for the women, $\bar { x } _ { 2 }$. She formulates the hypotheses as follows $\mathrm { H } _ { 0 } : \mu _ { 1 } = \mu _ { 2 }$ $\mathrm { H } _ { \mathrm { a } } : \mu _ { 1 } \neq \mu _ { 2 }$ and will reject the null hypothesis if $\bar { x } _ { 1 } - \bar { x } _ { 2 }$, the observed difference between the sample means is too large. She will use a two-means z-test. Identify the flaw in her methodology.

Suppose a Researcher Wants to Perform a Hypothesis Test to Compare