Problem 95

Given information

A group of transfer bound students wondered if they will spend the same mean amount on texts and supplies each year at their four-year university as they have at their community college. They conducted a random survey of  students at their community college and  students at their local four-year university. The sample means were  and , respectively. The population standard deviations are known to be  and , respectively. Conduct a hypothesis test to determine if the means are statistically the same.

Step-by-step explanation

The hypothesis testing in the required format as given in the problem is as follows:

 The null hypothesis can be stated as follows:

 The alternate hypothesis can be stated as follows:

The random variable is defined as the difference between the mean amount on texts and supplies each year at the four-year university and the community college.

 The problem requires the Normal distribution.

 To find the required statistic following algorithm is used:

1. Press  and twice  to select the tests
2. Press  and  to enter the stat list editor. 
3. Enter the given values as input as in the following display:

        The output display is as follows:

      The test statistic is .    

 Note the  which is .

 Using the previous information to sketch a picture of this situation. Labeled and scaled horizontal axis and shaded the region(s) corresponding to the  The graph is,

 The decisions and noted values are as follows:

        Decision: The decision is to not reject null hypothesis for .

        Reason for Decision: .

        Conclusion: At the  level of significance, there is not enough evidence to conclude that the mean costs of texts and supplies at community colleges and  j h              universities is different.

Hence, the hypothesis test is completed in format of given decision sheet.

The conclusion is not to reject the null hypothesis and at the level of significance because there is not enough evidence to conclude that the mean costs of texts and supplies at community colleges and universities is different.