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 test statistic for this hypothesis test would be ----- .
A)t x = 2.31
B)t x = 1.45
C)z x = 2.04
D)z x = 1.25

Question

Quizplus · Accepted Answer

The test statistic for this hypothesis test is calculated using the formula for a t-test because the population standard deviation is unknown and the sample size is small (n < 30). The formula is $t = \frac{\bar{x} - \mu}{(s/\sqrt{n})}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values: $t = \frac{764.2 - 753}{(34.5/\sqrt{20})}$ results in a t-value close to 1.45, making option B the correct choice.

Recently, Experian Reported That the Average Credit Score for a New-