Question

A company claims that it has over 50% community support for a new proposed chemical plant. A random sample of 100 residents found that 41 were in support of the plant with 59 being either being opposed or not sure. Is there enough evidence to show, at the α = 0.05 significance level, that the support for the plant is less than 50%?

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.50

H_a : p < 0.50

= x / n = 59 / 100 = 0.59

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.59 - 0.50 / [(0.50 * 0.50) / 100]

= 1.8

P-value = 0.9641

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to support the plant is less than 50% .