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. Use the traditional method or P-value method as indicated.
-A paint manufacturer wishes to compare the drying times of two different types of paint.
Independent random samples of 11 cans of type A and 9 cans of type B were selected and applied to similar surfaces. The drying times (in hours) were recorded. The summary statistics are as follows.
$$\begin{array} { c | c } \text { Type A } & \text { Type B } \\\hline \bar { x } _ { 1 } = 75.1 \mathrm { hrs } & \overline { \mathrm { x } } _ { 2 } = 63.1 \mathrm { hrs } \\\mathrm { s } _ { 1 } = 4.5 \mathrm { hrs } & \mathrm { s } _ { 2 } = 5.1 \mathrm { hrs } \\\mathrm { n } _ { 1 } = 11 & \mathrm { n } _ { 2 } = 9\end{array}$$
Use a 0.01 significance level to test the claim that the mean drying time for paint type A is equal to the mean drying time for paint type B. Use the P-value method of hypothesis testing.