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. $$\begin{array} { | c | c | } \hline \text { Women } & \text { Men } \\\hline \bar { x } _ { 1 } = 12.5 \mathrm { hrs } & \bar { x } _ { 2 } = 13.8 \mathrm { hrs } \\\hline s _ { 1 } = 39 . \mathrm { hrs } & s _ { 2 } = 5.2 \mathrm { hrs } \\\hline n _ { 1 } = 14 & n _ { 2 } = 17 \\\hline\end{array}$$ 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.