Question

Males and females were asked about what they would do if they received a $100 bill by mail, addressed to their neighbor, but wrongly delivered to them. Would they return it to their neighbor? Of the 69 males sampled, 59 said yes and of the 131 females sampled, 120 yes.

ON THE CALCULATOR TI-83 / TI-84

A: Does the data indicate that the proportions that said yes are different for males and females at a 5% level of significance?

B: Construct a 95% confidence interval for the difference in the two proportions (p1-p2)

Answer 1

Solution:

Hypothesis are

H0 : p₁ - p₂ = 0 vs H1: p₁ p₂

a)

Z test for two proportions ON THE CALCULATOR TI-83 / TI-84

Steps:

Press STAT and go to TESTS menu.

Then go to 2-PropZTest

x1: 59

n2: 69

x2: 120

n2: 131

p1 p2

Calculate

Output:

z = -1.336811708

p = 0.1812842299

Conclusion:

p value is greater than level of significance

Fail to reject H0

Data does NOT indicate that the proportions that said yes are different for males and females.

B)

Construct a 95% confidence interval for the difference in the two proportions (p1-p2)

Steps:

Press STAT and go to TESTS menu.

Then go to 2-PropZInt

x1: 59

n2: 69

x2: 120

n2: 131

C - Level : 0.95

Calculate :

Output:

(-0.1566 , 0.03472 )