A study was done about how often different age groups use their phones. When 258

Question

A study was done about how often different age groups use their phones. When 258 people in the age group 20-39 were surveyed, 69% brought their phones to bed with them. When 129 people in the age group 40-49 were asked the same question, 52% answered “yes”. Perform a hypothesis test at the 5% significance level to determine if there is a difference between proportions.

13. Null and Alternative Hypothesis
14. Test Statistic
15. Critical Value(s)
16. P-value
17. State the final conclusion that addresses the original claim

Explanation / Answer

Data:    

n1 = 258   

n2 = 129   

p1 = 0.69   

p2 = 0.52   

Hypotheses:    

Ho: p1 = p2    

Ha: p1 p2    

Decision Rule:    

= 0.05   

Lower Critical z- score =   -1.959963985

Upper Critical z- score = 1.959963985

Reject Ho if |z| >   1.959963985

Test Statistic:    

Average proportion, p = (n1p1 + n2p2)/(n1 + n2) = (258 * 0.69 + 129 * 0.52)/(258 + 129) = 0.633333333

q = 1 - p = 1 - 0.633333333333333 = 0.366666667

SE = [pq * {(1/n1) + (1/n2)}] = (0.633333333333333 * 0.366666666666667 * ((1/258) + (1/129))) = 0.051964011

z = (p1 - p2)/SE = (0.69 - 0.52)/0.0519640106028472 = 3.271494983

p- value = 0.001069805   

Decision (in terms of the hypotheses):    

Since 3.271494983 > 1.959963985 we reject Ho and accept Ha

Conclusion (in terms of the problem):    

There is sufficient evidence that the two population proportions are significantly different.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.