Question

A credit card company claims that the mean credit card debt for individuals is greater than $5,100.

Answer 1

Answer:

We conclude that that there is enough evidence to support the claim mean credit card debt for individuals is greater than $5,100.

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = $5,100

Sample mean, $\bar{x}$ = $ 5,270

Sample size, n = 27

Alpha, α = 0.10

Sample standard deviation, s = $550

a) First, we design the null and the alternate hypothesis

$H_{0}: \mu = 5100\text{ dollars}\\H_A: \mu > 5100\text{ dollars}$

We use one-tailed t test to perform this hypothesis.

b) Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{5270 - 5100}{\frac{550}{\sqrt{27}} } =1.606$

c) Now,

$t_{critical} \text{ at 0.10 level of significance, 26 degree of freedom } = 1.314$

Since,                    

$t_{stat} > t_{critical}$

d) We fail to accept the null hypothesis, and accept the alternate hypothesis.

e) We conclude that that there is enough evidence to support the claim mean credit card debt for individuals is greater than $5,100.