Question

According to a polling​ organization, 22% of adults in a large region consider themselves to be liberal. A survey asked 200 respondents to disclose their political​ philosophy: Conservative,​Liberal, And Moderate. Treat the results of the survey as a random sample of adults in this region. Do the survey results suggest the proportion is higher than that reported by the polling​organization? Use an alpha =0.05 level of significance.

75- Liberal
65- Moderate
61- Conservative

Answer 1

Explanation:

Using the proportion test

Null hypothesis: p <= 0.22

Alternative hypothesis: p > 0.22

Using the formula

z score = p - P /√ (P(1-P)/n)

Where p is 74/200= 0.37, P = 0.22, n = 200.

0.37-0.22 / √(0.22(1-0.22)/200)

0.15 / √(0.22(0.78)/200)

0.15 / √(0.1716/200)

0.15/ √0.000858

0.15 / 0.02929

= 5.1212

To help arrive at a conclusion, we have to find the p value, using a p value calculator at the 0.05 level of significant, the p value is less than 0.00001... Thus we would reject the null as there is sufficient statistical evidence to prove that the proportion is higher than that reported by the polling ​organization.