Question

a. According to a study conducted for Gateway Computers, 60% of men and 70% of women say that weight is an extremely/very important factor in purchasing a laptop computer. Suppose this survey was conducted using 374 men and 481 women. Do these data show enough evidence to declare that a significantly higher proportion of women than men believe that weight is an extremely/very important factor in purchasing a laptop computer? Use a 5% level of significance. b. Use these data to construct a 95% confidence interval to estimate the difference in population proportions on this question.

Answer 1

(a)

H0: Null hypothesis: P1 = P2

HA: Alternative hypothesis: P1 < P2

n1 = size of sample 1 = 374

p1 = proportion of sample 1 = 0.6

n2 = size of sample 2 = 481

p2 = proportion of sample 2 = 0.7

Q = 1 - P = 0.3437

Test statistic is:
Z = (p1 - p2)/SE

= (0.6 - 0.7)/0.0328 = - 3.0488

= 0.05

One tail Left side test

From Table, critical value of Z = - 1.64

Since the calculated value of Z = - 3.0488 is less tha critical value of Z = - 1.64, H0 is rejected.

Conclusion: These data show enough evidence to declare that a significantly higher proportion of women than men believe that weight is an extremely/ very important factor in purchasing a laptop.

(b)

From Table, criical value of Z = 1.96

95% Confidence interval:
(p1 - p2) Z SE

= (0.6 - 0.7) 1.96 X 0.0328

= -0.1 0.0643

= ( - 0.1643, - 0.9357)