Independent random samples taken on two university campuses revealed the following information concerning the average amount of money spent on textbooks during the fall semester. university a university bsample size 50 40average purchase $280 $250standard deviation $20 $23at * = .05, test to determine if, on the average, students at university a spend more on textbooks then the students at university b

So with the p value obtained and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group A is significantly lower than the mean for the group B.  

Step-by-step explanation:

The statistic to test the hypothesis is given by this formula:

Where t follows a t distribution with degrees of freedom

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 A

represent the sample size for group B

represent the sample mean for the group A

represent the sample mean for the group B

represent the sample standard deviation for group A

represent the sample standard deviation for group B

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 alternative hypothesis:

So with the p value obtained and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the mean of the group A is significantly lower than the mean for the group B.  

the equivalent expression are always the hardest ones but you look at the gcf also

step-by-step explanation: