Question

A well-known brokerage firm executive claimed that 20% of investors are currently confident of meeting their investment goals. An XYZ Investor Optimism Survey, conducted over a two week period, found that in a sample of 700 people, 26% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is larger than 20% at the 0.10 significance level.

The null and alternative hypothesis would be:

H0:p≤0.2
H1:p>0.2

H0:p=0.2
H1:p≠0.2

H0:μ=0.2
H1:μ≠0.2

H0:p≥0.2
H1:p<0.2

H0:μ≤0.2
H1:μ>0.2

H0:μ≥0.2
H1:μ<0.2

The test statistic is:  (to 3 decimals)

The p-value is:  (to 4 decimals)

Answer 1

Test Hypothesis :

H0: p ≤ 0.20

H1: p > 0.20

Test statistic :

Z = 3.969

P-value:

P= 0.000036 = 0.0000 = 0

Conclusion :

P-value is less than alpha=0.10 then conclude that reject H0.