Problem 93

Given information

A study is done to determine if students in the California state university system take longer to graduate, on average, than students enrolled in private universities. One hundred students from both the California state university system and private universities are surveyed. Suppose that from years of research, it is known that the population standard deviations are  years and  year, respectively. The following data are collected. The California state university system students took on average  years with a standard deviation of  The private university students took on average  years with a standard deviation of  

Step-by-step explanation

The solution sheet provided for the problem is used to do the hypothesis testing as follows:

The null hypothesis can be stated as follows:

The alternate hypothesis can be stated as follows:

 The random variable represents the difference in the times of mean it takes to graduate from the state university of California system and private universities.

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. CLEARLY, label and scale the horizontal axis and

shade the region(s) corresponding to the The graph is,

The decisions and noted values are as follows:

       Decision: Reject null when; do not reject null when.

       Reason for Decision: .

       Conclusion: At the level of significance, there is enough proof to conclude that the mean time it takes to graduate from California                     state universities is more than that of private universities.

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

The conclusion is to reject the null hypothesis and at the  level of significance, there is enough proof to conclude that the mean time it takes to graduate from California state universities is more than that of private universities.