The manager of a fund that provides loans for college students has estimated that the average monthly loan repayment for students borrowing

Question

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.

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3 months 2022-02-09T08:19:01+00:00 1 Answer 0 views 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