Problem 79

Given information

A student at a four-year college claims that means enrollment at four–year colleges is higher than at two–year colleges in the United States. Two surveys are conducted. Of the  two–year colleges surveyed, the mean enrollment was  with a standard deviation of . Of the  four-year colleges surveyed, the mean enrollment was  with a standard deviation of   

Step-by-step explanation

As given in the problem, A student at a four-year college claims that means enrollment at four–year colleges is higher than at two–year colleges in the United States. Two surveys are conducted. Of the  two–year colleges surveyed, the mean enrollment was  with a standard deviation of . Of the  four-year colleges surveyed, the mean enrollment was  with a standard deviation of   

Now, consider the following observations:

 The null hypothesis is defined as follows:

 The alternative hypothesis is stated as follows:

  The difference in the average number of English courses taken by males and females is denoted by .

   Student’s t (sample t-test, variances not pooled).

Test statistics    

The output has a value of  .  

Drawing a representation of the situation using the information from the last exercise.

The horizontal axis should be clearly labeled and scaled, and the region(s) matching to the should be shaded on the graph.

   Decision: Null hypothesis is rejected.

    There is insufficient evidence to establish that mean enrolment at four-year colleges is higher than at two-year colleges at the significance level.

Therefore,

No, the means are not statistically the same, there is no sufficient proof to conclude that mean enrollment at four-year colleges is higher than at two-year colleges.