Ask Question
11 October, 07:39

The manager of a fund that provides loans for college students has estimated that the average monthly loan repayment for students borrowing from the fund is $75.00. You are to test this estimate. You take a sample of 20 students and find that the mean monthly payment is $69.46 with a standard deviation of $9.78. Which of the following statements is true about this test?

a. The value of the test statistic is -.57; therefore, the null hypothesis is rejected for mean = 0.02.

b. The value of the test statistic is - 2.53; therefore, the null hypothesis is rejected for mean = 0.02.

c. The value of the test statistic is - 2.53; therefore, the null hypothesis is rejected for mean = 0.05 but not for mean = 0.02.

d. The value of the test statistic is -.57; therefore, the null hypothesis is rejected for mean = 0.05 but not for mean = 0.02.

+1
Answers (1)
  1. 11 October, 08:03
    0
    Step-by-step explanation:

    We would set up the hypothesis test.

    For the null hypothesis,

    µ = 75

    For the alternative hypothesis,

    µ ≠ 75

    Since the number of samples is 20 and no population standard deviation is given, the distribution is a student's t.

    Since n = 20,

    Degrees of freedom, df = n - 1 = 20 - 1 = 19

    t = (x - µ) / (s/√n)

    Where

    x = sample mean = $69.46

    µ = population mean = $75

    s = samples standard deviation = $9.78

    t = (69.46 - 75) / (9.78/√20) = - 2.53

    We would determine the p value using the t test calculator. It becomes

    p = 0.01

    Since alpha, 0.05 > than the p value, 0.01, then the null hypothesis is rejected.

    Therefore,

    The value of the test statistic is - 2.53; therefore, the null hypothesis is rejected for level of significance = 0.05
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “The manager of a fund that provides loans for college students has estimated that the average monthly loan repayment for students borrowing ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers