Question

A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit card debt of 20 residents in that town has a mean credit card debt of $3600 and a standard deviation of $391. At α=0.10, can the credit agency’s claim be supported, assuming this is a normally distributed data set?

Answer 1

Answer:

Claim is false

Step-by-step explanation:

Claim : A credit reporting agency claims that the mean credit card debt in a town is greater than $3500.

$H_0:\mu \leq 3500\\H_a:\mu = 3500$

n = 20

Since n <30

So we will use t test

Formula : $t =\frac{x-\mu}{\frac{s}{\sqrt{n}}}$

s = standard deviation = 391

x = 3600

n = 20

$t =\frac{3600-3500}{\frac{391}{\sqrt{20}}}$

$t =1.14$

Degree of freedom = n-1 = 20-1 = 19

α=0.10

So, using t table

$t_({\frac{\alpha}{2},d.f.})$ = 1.72

t critical > t calculated

So we accept the null hypothesis

Hence we reject the claim that the mean credit card debt in a town is greater than $3500.