Question

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. 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 original report. Based on previous studies, use a population standard deviation σ = $1,000.

(a)

State the null and alternative hypotheses.

H₀: μ = 3,173 , H_a: μ ≠ 3,173 or

H₀: μ ≤ 3,173 , H_a: μ > 3,173 or

H₀: μ < 3,173 , H_a: μ ≥ 3,173 or

H₀: μ > 3,173, H_a: μ ≤ 3,173 or

H₀: μ ≥ 3,173 , H_a: μ < 3,173 or

(b)

What is the test statistic for a sample of 185 undergraduate students with a sample mean credit card balance of $3,315? (Round your answer to two decimal places.)

What is the p-value for a sample of 185 undergraduate students with a sample mean credit card balance of $3,315? (Round your answer to four decimal places.)

p-value =

(c)

Using a 0.05 level of significance, what is your conclusion?

Do not reject H₀. There is sufficient evidence to conclude that the current population mean credit card balance for undergraduate students has increased compared to the previous all-time high of $3,173 reported in the original report.Reject H₀. There is insufficient evidence to conclude that the current population mean credit card balance for undergraduate students has increased compared to the previous all-time high of $3,173 reported in the original report.    Reject H₀. There is sufficient evidence to conclude that the current population mean credit card balance for undergraduate students has increased compared to the previous all-time high of $3,173 reported in the original report.Do not reject H₀. There is insufficient evidence to conclude that the current population mean credit card balance for undergraduate students has increased compared to the previous all-time high of $3,173 reported in the original report.

Answer 1

ANSWER:

given

  

a)   

b) n = 185, = & 3345

test statistic

  

Z  = 2.34

c) p - value = P (Z>Z) = P(Z>2.34)

= 0.0096

c)

P - value < ,

Reject , there is sufficient evidence to conclude that current polulation mesan credit card balance for undergraduate student has increase compared to the previous all time high of $ 3173 reported in the original report .