Test the Indicated Claim About the Means of Two Populations

Essay

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. Use the traditional method or P-value method as indicated.
-A researcher was interested in comparing the amount of time (in hours) spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The summary statistics are as follows.
$$\begin{array} { l | c } \quad \text { Women } & \text { Men } \\\hline \overline { \mathrm { x } } _ { 1 } = 12.1 \mathrm { hr } & \overline { \mathrm { x } } _ { 2 } = 14.2 \mathrm { hr } \\\mathrm { s } _ { 1 } = 3.9 \mathrm { hr } & \mathrm { s } _ { 2 } = 5.2 \mathrm { hr } \\\mathrm { n } _ { 1 } = 14 & \mathrm { n } _ { 2 } = 17\end{array}$$
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. Use the traditional method of hypothesis testing.