Question

Recently, Experian reported that the average credit score for a new-car loan was 753. Suppose Ally Financial, a bank holding company that finances car loans, would like to test the hypothesis that the average credit score has increased since the Experian report. A random sample of 20 new-car loans had an average credit score of 764.2 with a sample standard deviation of 34.5. Ally Financial would like to set α = 0.05. The p-value for this hypothesis test would be ________.

Answer 1

Solution:

Here, we have to use one sample t test for the population mean.

The null and alternative hypotheses are given as below:

H₀: µ = 753 versus H_a: µ > 753

This is an upper tailed test.

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

From given data, we have

µ = 753

Xbar = 764.2

S = 34.5

n = 20

df = n – 1 = 19

t = (Xbar - µ)/[S/sqrt(n)]

t = (764.2 - 753)/[ 34.5/sqrt(20)]

t = 1.4518

P-value = 0.0817

(by using t-table)

The p-value for this hypothesis test would be 0.0817.