Question

A random sample of 200 economics majors show that 90 percent of those sampled love statistics. Another random sample of 100 finance majors is taken and 85 percent of those love statistics. Using a 0.05 level of significance, test the claim that a higher proportion of economics majors love statistics that finance majors.

Answer 1

H0: p1 = p2

Ha: p1 > p2

pooled proportion = [ 1 * n1 + 1 * n2 / ( n1 + n2) ]

= [ 0.90 * 200 + 0.85 * 100 / (200 + 100) ]

= 0.8833

Test statistics

z = (1 - 2) / sqrt [ ( 1 - ) * ( 1 / n1 + 1 / n2) )

= (0.90 - 0.85) / sqrt ( 0.8833 ( 1 - 0.8833) * ( 1 / 200 + 1 / 100) )

= 1.27

From Z table,

Critical value at 0.05 significance level = 1.645

Since test statistics < 1.645 , fail to reject H0.

We conclude that we fail to support the claim that a higher proportion of economics majors

love statistics that finance majors.