Question

a credit card company claims that the mean credit card debt for individuals is greater than 4700.00 you want to test this claim. you find that a random sample of 38 cardholders has a mean credit card balance of 4873.00 and a standard deviation of 575.00 at a=0.05

Answer 1

Given:

Sample size = n = 38

Sample mean = = 4873

Standard deviation = s = 575

Significance level = = 0.05

Claim : A credit card company claims that the mean credit card debt for individuals is greater than 4700.

Hypothesis test :

The null and alternative hypothesis is

Ho : = 4700

Ha : > 4700

Test statistic :

t = ( - ) / s/√n

= (4873 - 4700) / 575 /√38

= 1.855

t = 1.855

Degree of freedom = df = n-1 = 38-1 = 37

P-value :

P-value corresponding to t = 1.855 with df = 37 is

P(t > 1.855) = 0.0358

Since P-value < = 0.05, we reject the null hypothesis.

Dicision : Reject the null hypothesis.

Conclusion : There is sufficient evidence to conclude that a credit card company claims that the mean credit card debt for individuals is greater than 4700 at = 0.05