Question

you have been asked to study the mean yearly tuition at private four-year colleges and universities across the United States. You are interested in making some decisions concerning this population parameter. You select a random sample of 50 universities from this population. The mean tuition at these universities is found to equal $18,205. You still have reason to believe that the population standard deviation of the tuition amounts is known to equal $9,000. At both the 5% and 10% levels of significance, is the mean tuition at this population of universities less than $20,000? In your memo, if appropriate, comment upon the effect of the change in the significance level on your decision.

Please provide an explanation of your answer!

Answer 1

At alpha = 0.10 L.O.S

Test Statistics

The z-statistic is computed as follows:

At alpha = 0.10 L.O.S

(5) Conclusion

( i ) It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the the mean tuition at this population of universities less than $20,000  at the 0.05 significance level.

( ii ) It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the  the mean tuition at this population of universities less than $20,000 at the 0.10 significance level.