Question

In a study entitled How Undergraduate Students Use Credit Cards, Sallie Mae reported that undergraduate students have a mean credit card balance of $3173. This figure was an all-time high and had increased drastically over the previous five years. Assume that a current study is being conducted to determine whether it can be concluded that the mean credit card balance for undergraduate students has continued to increase compared to the April 2009 report (i.e. greater than 3173). Based on previous studies, use a population standard deviation, σ = $1000. A random sample of 180 undergraduate students was taken and the sample mean credit card balance was $3,325. Let α = 0.01.

1. state the null & alternative hypothesis

2. construct the rejection region

3. calculate test statistic (z)

4. state decision to reject or not to reject

Answer 1

Solution :

= 3173

=3325

= 1000

n =180

This is the right  tailed test .

1 ) The null and alternative hypothesis is ,

H₀ :   = 3173

H_a : > 3173

2 ) = 0.01

critical value = 2.33

The rejection region for this right-tailed test is R = (z : z > 2.33 )

3 )Test statistic = z

= ( - ) / / n

= (3325-3173) /1000 / 180

= 2.039

P(z > 2.039) = 1 - P(z < 2.039) = 1 - 0.9793 = 0.0207

P-value = 0.0207

p = 0.0207 ≥ 0.01, it is concluded that the null hypothesis is not rejected.

4 ) do not reject

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