Question

A well-known brokerage firm executive claimed that 90% 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 800 people, 82% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is smaller than 90% at the 0.01 significance level.

The null and alternative hypothesis would be:

H0:μ=0.9H0:μ=0.9
H1:μ≠0.9H1:μ≠0.9

H0:p≤0.9H0:p≤0.9
H1:p>0.9H1:p>0.9

H0:μ≤0.9H0:μ≤0.9
H1:μ>0.9H1:μ>0.9

H0:p=0.9H0:p=0.9
H1:p≠0.9H1:p≠0.9

H0:μ≥0.9H0:μ≥0.9
H1:μ<0.9H1:μ<0.9

H0:p≥0.9H0:p≥0.9
H1:p<0.9H1:p<0.9

The test is:

two-tailed

left-tailed

right-tailed

The test statistic is:  (to 3 decimals)

The p-value is:  (to 4 decimals)

Based on this we:

• Reject the null hypothesis
• Fail to reject the null hypothesis

Answer 1

Solution-

1) The null and alternative hypothesis would be

Ho : p ≥ 0.9

H1 : p < 0.9

2) The test is -

Left-tailed test

3) The test statistic is -

Z = -7.542

4) The p-value is - 0.00001

p = 0.0000 ----- ( 4 decimals )

5)Based on this we-

Reject the Null Hypothesis.

◆ Test calculation and results-