Question

According to a study conducted by a major computer company, 59% 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.

Answer 1

Let p1 be the proportion of mean and p2 be the proportion of women.

H0: p1 = p2

Ha: p1 < p2

Polled proportion = (n1 * p1 + 22 * p2) / (n1 + n2)

= (374 * 0.59 + 481 * 0.70) / (374 + 481)

= 0.6519

Test statistics

z = p1 - p2 / Sqrt [ (1 - ) * sqrt( 1 / n1 + 1/ n2) ]

= (0.59 - 0.70) / Sqrt [ 0.6519 * 0.3481 * (1 / 374 + 1/481) ]

= -3.35

This is test statistics value.

Critical value at 0.05 level is -1.645.

Since test statistics value < -1.645, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have enough evidence to support the claim.