Question

A credit card company claims that the mean credit card debt for individuals is greater than S4,900. You want to test this claim. You find that a random sample of 30 cardholders has a mean credit card balance of $5,157 and a standard deviation of $625. At ?= 0.10, can you support the claim? Complete parts (a) through (e) below. Assume the population is normally distributed (a) Write the claim mathematically and identify Ho and Ha Which of the following correctly states Ho and Ha? A. Ho ? > $4.900 Ha : ? $4.900 D. Ho : ? > $4,900 Ha HsS4,900 ° C. H0: ?= $4.900 Ha : ? $4.900 OF. H0.? $4.900 Ha H<S4,900 ?. ??: $4,900 Ha : ? > $4,900 Ho.? $4.900 Ha : ? > $4,900 E. (b) Find the critical value(s) and identify the rejection region(s) What is(are) the critical value(s). tn? (Use a comma to separate answers as needed. Round to three decimal places as needed.) Determine the rejection region(s). Select the correct choice below and fill in the answer box(es) within your choice (Round to three decimal places as needed.) OB. t and t>

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test:
? : Mean of population
H₀ : ? = 4900
H_A : ? > 4900

Hypothesis test results:

Mean	Sample Mean	Std. Err.	DF	T-Stat	P-value
?	5157	114.10887	29	2.2522352	0.016

Hence,

a) Option E is correct.

b) Critical value = 1.311

Rejection region: Option A; t > 1.311

c) Test statistic = 2.25

d) Option D is correct.

e) Option C is correct.