Question

Instructions: Round all your math steps to two decimal places just like I have been doing in class.

In a study entitled How Undergraduate Students Use Credit Cards, it was reported that undergraduate students have a mean credit card balance of $3,173 (Sallie Mae, April 2009). This figure was an all-time high and had increased 44% over the previous five years. Assume that a current study is being conducted to determine if it can be concluded that the mean credit card balance for undergraduate students has continued to increase compared to the April 2009 report. Based on previous studies, use a population standard deviation σ=$1,000.

a. What is the p-value for a sample of 180 undergraduate students with a sample mean credit card balance of $3,325? (Round to four decimal places). Answer

b. Using a .05 level of significance, what is your conclusion? Answer choices - (Reject the null hypothesis) (do not reject the null hypothesis)

Answer 1

a)

x̅ (sample mean) = 3325

n (sample size) = 180

σ (population standard deviation) = 1000.

μ = 3173

Test Statistic =  x - μ/ σ / √n = 2.0392

Test Statistic =2.0392

α = 0.05

Left-tailed area corresponding to z-score of -2.0392 = 0.02071

Right-tailed area corresponding to z-score of 2.0392 = 0.02071

p-value = Left-Tailed Area + Right-Tailed Area = 0.04142

b)

p-value is less than or equal to α.

If p-value is less than or equal to α then reject the null hypothesis.