Question

According to an estimate, the average total parent and student debt for new college graduates was $34,400 in 2010–11 (Time, October 31, 2011). A random sample of 500 of this year’s graduates showed that their average such debt is $39,000 with a standard deviation of $5500. Do the data provide significant evidence at a 3% significance level to conclude that the current average total parent and student debt for new graduates is higher than $34,400? Use both the p-value approach and the critical-value approach. Use the p-value approach. Use the t distribution table to find a range for the p-value. Enter the exact values for the range

_______ < p-value<_______

Use the critical-value approach. Round your observed value to four decimal places, and your critical value to two decimal places.

Observed value =_______
Critical value =____

Answer 1

Solution:

This a right (One) tailed test.

The null and alternative hypothesis is,  

Ho: 34400

Ha: 34400

The test statistics,

t =( - )/ (s /n)

= ( 39000 - 34400 ) / ( 5500 / 500 )

= 18.702

P-value = 0.00001

0.0< p-value< 0.1

Critical value of  the significance level is α = 0.03, and the critical value for a right-tailed test is

= 1.885

Since it is observed that t = 18.702 > = 1.885, it is then concluded that the null hypothesis is rejected.

Observed value =18.702
Critical value =1.885