A study is done by a community group in two neighboring colleges to determine which one graduates students with more math classes. College A samples 11 graduates and finds the mean is 4 math classes with a standard deviation of 1.5 math classes. College B samples 9 graduates and finds the mean is 3.5 math classes with a standard deviation of 1 math class. The community group believes that a student who graduates from college A has taken more math classes, on the average. Test at a 10% significance level. Assume the requirements for a valid hypothesis test are satisfied.

The p value for this case would be:

The p value is higher than the significance level so then we can conclude that we can FAIL to reject the null hypothesis and then the true mean for group A is not significantly higher than the mean for B

Step-by-step explanation:

Information given

represent the mean for sample A

represent the mean for sample B

represent the sample standard deviation for A

represent the sample standard deviation for B  

sample size for the group A

sample size for the group B  

Significance level provided

t would represent the statistic

Hypothesis to test

We want to verify if the student who graduates from college A has taken more math classes, on the average, the system of hypothesis would be:  

Null hypothesis:  

Alternative hypothesis:  

The statistic is given by:

(1)  

And the degrees of freedom are given by  

Replacing we got:

The p value for this case would be:

The p value is higher than the significance level so then we can conclude that we can FAIL to reject the null hypothesis and then the true mean for group A is not significantly higher than the mean for B

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