Test the Indicated Claim About the Means of Two Populations

Test the indicated claim about the means of two populations. Assume that the two samples are
independent simple random samples selected from normally distributed populations. Do not
assume that the population standard deviations are equal. $$\begin{array} { | l | l | } \hline { \text { Women } } & { \text { Men } } \\\hline \bar { x } _ { 1 } = 12.5 \mathrm { hrs } & \bar { x } _ { 2 } = 13.8 \mathrm { hrs } \\\hline s _ { 1 } = 3.9 \mathrm { hrs } & s _ { 2 } = 5.2 \mathrm { hrs } \\\hline n _ { 1 } = 14 & n _ { 2 } = 17 \\\hline\end{array}$$ Use a 0.05 significance level to test the claim that the mean amount of time spent watching
television by women is smaller than the mean amount of time spent watching television by
men. Include your null and alternative hypotheses, the test statistic, P-value or critical value(s),
conclusion about the null hypothesis, and conclusion about the claim in your answer.