Question

In 1941, 48% of 674 Americans surveyed favored admitting Hawai‘i as a state, while in 1946, 60% of 739 Americans surveyed did.

(a) Test the claim that more Americans favored admitting Hawai‘i as a state in 1946 than in 1941 at a significance level of .05.

(b) Test the claim that the proportion of Americans who favored admitting Hawai‘i as a state was at least 8 percentage points higher in 1946 than it was in 1941 at a significance level of .05.

Answer 1

Answer:

Given,

Ho : p1 = p2

Ha : p1 < p2

pooled proportion p = (x1+x2)/(n1+n2)

substitute values

= (323.52 + 443.4 ) / ( 674 + 739 )

= 0.5428

consider,

test statistic z = (p1 - p2)/sqrt(p(1-p)(1/n1 + 1/n2))

= (0.48 - 0.60)/sqrt(0.5428(1-0.5428)(1/674 + 1/739))

z = -4.523

Here at 0.05 significance level, z value is 1.645

Here we observe that, test statistic < critical value, so we reject Ho.

So we have sufficient evidence.

b)

Ho : p1-p2 >= 0.08

Ha : p1-p2 < 0.08

consider,

test statistic z = (p1 - p2)/sqrt(p(1-p)(1/n1 + 1/n2))

On substituting values & solving then we get

test statistic z = - 7.59

Here we observe that, test statistic < critical, so we reject Ho.

And we have sufficient evidence.