Question

Two surveys were done regarding credit card debt. Survey #1: Five years ago the average credit card debt was $6618. ​Survey #2:The average credit card debt for a recent year was $9205. Assume sample sizes of 35 were used and the standard deviations of both samples were $1928. Is there enough evidence to believe that the average credit card debt has changed in the past 5 years? Assume a 5% Level of Significance

Answer 1

There is enough evidence to believe that the average credit card debt has changed in the past 5 years

Explanation:

We are to compare the means of two samples. Since only sample std deviations are used, we have to use t test for this hypothesis

H0: Means are equal

Ha: Means are not equal

(Two tailed test at 5% )

Difference between means
`M1-M2 = -2587`

Std deviation combined = 3856

Std error for difference = 460.88

t statistic
`= -2587/460.88=-5.613`

p value =0

Since p <0.05 reject null hypothesis.

There is enough evidence to believe that the average credit card debt has changed in the past 5 years