The Department of Education would like to test the hypothesis that the average d
ID: 2931665 • Letter: T
Question
The Department of Education would like to test the hypothesis that the average debt load of graduating students with a Bachelor's 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. Which one of the following statements is true?
Because the p-value is greater than , we fail to reject the null hypothesis and conclude that the average debt load is equal to $17,000.
Because the p-value is less than , we reject the null hypothesis and conclude that the average debt load is equal to $17,000.
Because the p-value is less than , we fail to reject the null hypothesis and conclude that the average debt load is not equal to $17,000.
Because the p-value is greater than , we fail to reject the null hypothesis and cannot conclude that the average debt load is not equal to $17,000.
Because the p-value is greater than , we fail to reject the null hypothesis and conclude that the average debt load is equal to $17,000.
Because the p-value is less than , we reject the null hypothesis and conclude that the average debt load is equal to $17,000.
Because the p-value is less than , we fail to reject the null hypothesis and conclude that the average debt load is not equal to $17,000.
Because the p-value is greater than , we fail to reject the null hypothesis and cannot conclude that the average debt load is not equal to $17,000.
Explanation / Answer
Solution:
Test Hypothesis:
H0 : = $17000
H1 : $17000
Test Statistic:
Z = x - /(/n)
= 18200- 17000/(4200/34)
= 1.67
P-value = 0.0949
P-value = 0.0949 in this context is greater than 0.05, so the null hypothesis is not rejected at 5% level of significance.
There is insufficient evidence to indicate that the average debt load of graduating students with a Bachelor's degree is not equal to $17,000. The result is not statistically significant.
The option is D.Because the p-value is greater than , we fail to reject the null hypothesis and cannot conclude that the average debt load is not equal to $17,000.
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