Question

A pollster claims that Socialist proportion of registered Socialist voters in his country is lower than 0.05. A random sample of size 1000 registered voters revealed that the number of Socialists was 40. Test the relevant hypotheses at the 1% significance level.

Answer 1

Solution:

Given:

Claim: Socialist proportion of registered Socialist voters in his country is lower than 0.05.

Sample size = n =1000

x = 40

thus

significance level = 0.01

Step 1) State H0 and H1:

H0: p = 0.05 Vs H1: p < 0.01

Step 2) Test statistic:

Step 3) z critical value:

significance level = 0.01

look in z table for area = 0.0100 or its closest area and find z value.

Area 0.0099 is closest to 0.0100 and it corresponds to -2.3 and 0.03

thus z critical value = -2.33

Step 4) Decision Rule:
Reject null hypothesis ,if z  test statistic value < z critical value = -2.33 , otherwise we fail to reject H0.

Since z  test statistic value = -1.45 > z critical value = -2.33, we fail to reject H0.

Step 5) Conclusion:

At 1% significance level , we do not have sufficient evidence to support the claim that: Socialist proportion of registered Socialist voters in his country is lower than 0.05.