Question

According to the government lending institute Sallie Mae, students graduating college in United States have an average credit card debt of $6,130 with a standard deviation of $840. A random sample of 27 graduating seniors was selected, and their average credit card debt was found to be $5,760. Does this sample provide enough evidence to challenge the findings by Sallie Mae? α = 0.05. What is the decision?

Group of answer choices

There is not enough evidence to prove that average debe is different than $6,130.

There is enough evidence to prove that average debt is lower than $6,130.W owners keep cars less than 85,000 miles before trading in.

There is enough evidence to prove that average debt is dfferent than $6,130.

There is enough evidence to prove that average debt is higher than $6,130

Answer 1

The null and alternative hypothesis

6130

І: ОН

Ha:
$1596036220677_blob.png$6130

Test statistic

$z= \frac{\bar{X}-\mu }{\sigma /\sqrt{n}}$

$= \frac{5760-6130 }{840 /\sqrt{27}}$

= -2.29

For $\alpha$ =0.05 , two tailed critical value of z is

zc =1.96

Since I z I = 2.29 > 1.96

We reject H0

Answer is

There is enough evidence to prove that average debt is different than $ 6130