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.

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

Answers ( )

    0
    2022-02-09T08:20:58+00:00

    Answer:

    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

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )