Question

Reconsider the study described in activity 16-12. The nellie mae organization found that in random sample of 1413 undergraduate students taken in 2004, 76% of the students sampled had a credit card. Conduct a significance test of whether this sample result provides strong evidence that more than 75% of all undergraduate college students in the u.s had a credit card in 2004. Report the hypothesis test statistic, and p value. Also check the technical conditions of the test and summarize your conclusion

Answer 1

H0: p ? 75%
Null Hypothesis: The percentage of undergraduate students with credit cards is less or equal to 75%.
H1: p > 75%
Alternative Hypothesis: Over 75% of the undergraduates have credit cards.

n = 1413 || p = 76% --> p = x/n --> x = pn = 1413*76% = 1074



Z₀ = (1074 - 1413*75%)/(sqrt(1413*75%*25%)
Z₀ = 0.88

P value = 1 - ?(Z₀)
P value = 1 - ?(0.88)
P value = 1 - 0.810570
P value = 0.189430

zalpha = 1.65

0.88>1.65 fail to reject