Arandom sample of n1 =12 students majoring in accounting in a college of business has a mean grade-point average of 2.70 (where A = 4.0) with a sample standard deviation of 0.40. For the students majoring in computer information systems, a random sample of n2 = 10 students has a mean grade-point average of 2.90 with a standard deviation of 0.30. The grade-point values are assumed to be normally distributed. Test the null hypothesis that the mean-grade point average for the two categories of students is not different, using the 5 percent level of significance.

We accept the null hypothesis that the mean gpa's are equal, with the 5 percent level of significance.

Step-by-step explanation:

We have these following hypothesis:

Null

Equal means

So

Alternative

Different means

So

Our test statistic is:

In which are the sample means, are the sample sizes and are the standard deviations of the sample.

In this problem, we have that:

So

What to do with the null hypothesis?

We will reject the null hypothesis, that is, that the means are equal, with a significante level of if

In which v is the number of degrees of freedom, given by

Applying the formula in this problem, we have that:

So, applying t at the t-table at a level of 0.975, with 20 degrees of freedom, we find that

We have that

Which is lesser than t.

So we accept the null hypothesis that the mean gpa's are equal, with the 5 percent level of significance.

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