A random sample of 15 observations from the first population revealed a sample mean of 350 and a sample standard deviation of 12. A random sample of 17 observations from the second population revealed a sample mean of 342 and a sample standard deviation of 15. At the .10 significance level, what is the p-value for comparing the means, given that the variances are equal.

And now we can calculate the p value using the altenative hypothesis:

If we compare the p value obtained and using the significance level assumed we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.    

Step-by-step explanation:

When we have two independent samples from two normal distributions with equal variances we are assuming that  

And the statistic is given by this formula:

Where t follows a t distribution with degrees of freedom and the pooled variance is given by this formula:

This last one is an unbiased estimator of the common variance

The system of hypothesis on this case are:

Null hypothesis:

Alternative hypothesis:

Or equivalently:

Null hypothesis:

Alternative hypothesis:

Our notation on this case :

represent the sample size for group 1

represent the sample size for group 2

represent the sample mean for the group 1

represent the sample mean for the group 2

represent the sample standard deviation for group 1

represent the sample standard deviation for group 2

First we can begin finding the pooled variance:

And the deviation would be just the square root of the variance:

And now we can calculate the statistic:

Now we can calculate the degrees of freedom given by:

And now we can calculate the p value using the altenative hypothesis:

If we compare the p value obtained and using the significance level assumed we have so we can conclude that we have enough evidence to FAIL to reject the null hypothesis.    

i think it might be a but you might want a second opinion