Question

According to a study conducted by ABODO, about 70% of all college students use an online dating app. Suppose you want to know if Harvard students are similar to their national peers. You ask a random sample of 125 Harvard students and find that 78 of them use an online dating app.

a. Does this sample provide significant evidence at the ? = .05 level that the true proportion of Harvard students that use an online dating app is different than the ABODO estimate? Conduct a hypothesis test to justify your answer.

b. Give an interpretation in context for the p-value that you calculated in part a.

c. Your colleague constructed a confidence interval based on your sample and found that it didn’t include 0.7. Give an example of a confidence level they might have used. Justify your answer.

Answer 1

X = 78 and n = 125

P = 78/125 = 0.624

a)

alpha = 0.05

Hypothesis:

H0: P0 = 0.70

Ha: P0 not = 0.70(Two tailed)

Test:

Z = (P - P0)/SQRT(P0(1-P0)/n) = (0.624-0.70)/SQRT(0.70*0.3/125)

= -1.8542

Zcritical,at alpha=0.05

Zcritical=-1.96 (from Z-table)

since,Z>Zcritical,we fail to reject Ho

There is insuffient evidence to support the claim that the True proportion of CU stuydent that use an online dating app is different than the ABODO

b)

p-valve =0.0643 (from Z-table)

There is about 6.43% chance that the true propotion of ifequal to 70%

c)

The confidence level will be 90%,as 0.70 is outside the confidence interval

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