Questions: Test whether people with a specific genetic marker are more likely to have suffered from clinical depression than people without the genetic marker, using the information that 40% of the 40 people in a sample with the genetic marker have had clinical depression while 16% of the 775 people in the sample without the genetic marker have had clinical depression. Use subscripts 1 for yes these people have the genetic marker and 2 for no these people do not have the genetic market. (a) Find the relevant sample proportions in each group and the pooled proportion. Round your answers to three decimal places, if necessary. p̂₁=0.400 p̂₂=0.160 p̂=0.172 (b) State the null and alternative hypotheses. (c) Give the test statistic and the p-value. Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.

Test whether people with a specific genetic marker are more likely to have suffered from clinical depression than people without the genetic marker, using the information that 40% of the 40 people in a sample with the genetic marker have had clinical depression while 16% of the 775 people in the sample without the genetic marker have had clinical depression.

Use subscripts 1 for yes these people have the genetic marker and 2 for no these people do not have the genetic market.
(a) Find the relevant sample proportions in each group and the pooled proportion.

Round your answers to three decimal places, if necessary.

p̂₁=0.400
p̂₂=0.160
p̂=0.172

(b) State the null and alternative hypotheses.

(c) Give the test statistic and the p-value.

Round your answer for the test statistic to two decimal places and your answer for the p-value to three decimal places.

Transcript text: Test whether people with a specific genetic marker are more likely to have suffered from clinical depression than people without the genetic marker, using the information that $40 \%$ of the 40 people in a sample with the genetic marker have had clinical depression while 16\% of the 775 people in the sample without the genetic marker have had clinical depression. Use subscripts 1 for yes these people have the genetic marker and 2 for no these people do not have the genetic market. (a) Find the relevant sample proportions in each group and the pooled proportion. Round your answers to three decimal places, if necessary. \[ \begin{array}{l} \hat{p}_{1}=0.400 \\ \hat{p}_{2}=0.160 \\ \hat{p}=0.172 \end{array} \] (b) State the null and alternative hypotheses. (c) Give the test statistic and the $p$-value. Round your answer for the test statistic to two decimal places and your answer for the $p$-value to three decimal places.