Question

The average credit card debt for a recent year was $9525. Five years earlier the average credit card debt was $8904. Assume sample sizes of 25 were used and the population standard deviations of both samples were $883. Is there evidence to conclude that the average credit card debt has increased? Use  .

a. State the hypotheses.
b. Find the critical value.
c. Compute the test statistic.
d. Make the decision.
e. Summarize the results.

Answer 1

Solution:

This a right (One) tailed test.

a)

The null and alternative hypothesis is,  

Ho: $\mu$ $\leq$ 9525

Ha: $\mu$ 9525

b)

Critical value of  the significance level is α = 0.05, and the critical value for a right-tailed test is

$Z_{c}$ = 1.64

c)

The test statistics,

Z =( $\bar x$ - $\mu$ )/ ($\sigma$/$\sqrt{}$n)

= ( 8904 - 9525 ) / ( 883 / $\sqrt{}$ 25 )

= -3.52

d)

Since it is observed that ∣z∣=3.52 > zc=1.1.64, it is then concluded that the null hypothesis is rejected.

e)

There is evidence to conclude that the average credit card debt has increased. at 0.05 level of significance.