Question

A credit card company claims that the mean credit card debt for individuals is greater than $ 5 comma 300. You want to test this claim. You find that a random sample of 34 cardholders has a mean credit card balance of $ 5 comma 554 and a standard deviation of $ 650. At alpha equals 0.10?, can you support the? claim? Complete parts? (a) through? (e) below. Assume the population is normally distributed

Answer 1

Given data

population mean

Sample size (n)=34

Sample mean

sample standars daviation (S)=650

here the claim is the population mean is greater than 5300 that is

so hypothesis will be

test statistic will be

Now probablity value

since it is a upper tailed test so the probablity value will be p(X>5300)=1-p(X<5300)

so from the probablity distribution table for Z score we vae the left side area to the point Z=2.28 which represents the probablity for Z<5300 is

p(X<5300)=0.9887

so P(X>5300)= 1-0.9887=0.0113

now for making decision

given that

the Z criticle value for this criticle region foer upper tail test is

Since so the Z will lie above the criticle region hence we can say that we have enough evidence to reject the null hypothesis

conclusion As the null hypothesis is rejected so we can say that we have enough evidence to support the claim that the mean credit card debt for individual is greater than 5300