Please show work. Suppose that the Department of Education would like to test th
ID: 3063608 • Letter: P
Question
Please show work.
Suppose that the Department of Education would like to test the hypothesis that the average debt load of graduating students with a Bachelors degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The Department of Education would like to set =0.05. What is the conclusion for this hypothesis test? A. Since the absolute value of the test statistic is less than the absolute value of the critical value, we can conclude that the average student O B. Since the absolute value of the test statistic is more than the absolute value of the critical value, we cannot conclude that the average student ° C. Since the absolute value of the test statistic is more than the absolute value of the critical value, we can conclud that te average student D. Since the absolute value of the test statistic is less than the absolute value of the critical value, we cannot conclude that the average student debt load is not equal to $17,000 debt load is not equal to $17,000 debt load is not equal to $17,000 debt load is not equal to $17,000Explanation / Answer
sample mean is X¯=18200 and the known population standard deviation is =4200, and the sample size is n = 34
(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
Ho: =17000
Ha: 17000
This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.
(2) Rejection Region
Based on the information provided, the significance level is =0.05, and the critical value for a two-tailed test is zc=1.96.
(3) Test Statistics
The z-statistic is computed as follows:
z = [ (X¯0) / (/n) ]
z = [ (1820017000) / ( 4200/34) ]
Z =1.667
(4) Decision about the null hypothesis
Since it is observed that z=1.667 |zc|=1.96, it is then concluded that the null hypothesis is not rejected.
Answer :- Option "D" is correct.
The absolute value of the test statisticis less than the absolute value of critical value. So we can not concluded that the average student debt load is not equal to $17000