Question

A random sample of stipends of teaching assistants in economics is listed. Is there sufficient evidence at the a = 0.05 level to conclude that the average stipend differs from $15,000? The stipends listed (in dollars) are for the academic year.

14,500 17,500 12,500 13,856

13,685 12,919 14,500 11,481

18,108 11,783 16,838 14,500

A) Yes. There is enough evidence to conclude that the average stipend differs from $15,000.

B) No. There is not enough evidence to conclude that the average stipend differs from $15,000.

C) There is not enough information to draw a conclusion.

Answer 1

From the given sample data : Sampel size=n=12

Sample mean=

Sample standard deviation=

The null and alternative hypothesis is ,

The test is two-tailed test.

Now , df=degrees of freedom=n-1=12-1=11

The critical values are , ; Form t-table

The test statistic is ,

Decision : Here , the value of the test statistic does not lies in the rejection region.

Therefore , fail to reject Ho.

Conclusion :

B) No. There is not enough evidence to conclude that the average stipend differs from $15,000.