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 400 people, 21% 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 0.005 significance level.

The null and alternative hypothesis would be:

H0:p≤0.2H0:p≤0.2
H1:p>0.2H1:p>0.2

H0:μ=0.2H0:μ=0.2
H1:μ≠0.2H1:μ≠0.2

H0:p≥0.2H0:p≥0.2
H1:p<0.2H1:p<0.2

H0:μ≤0.2H0:μ≤0.2
H1:μ>0.2H1:μ>0.2

H0:p=0.2H0:p=0.2
H1:p≠0.2H1:p≠0.2

H0:μ≥0.2H0:μ≥0.2
H1:μ<0.2H1:μ<0.2

The test is:

two-tailed

right-tailed

left-tailed

The test statistic is: (to 3 decimals)

The p-value is: (to 4 decimals)

Based on this we:

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

Box 1: Select the best answer

Box 2: Select the best answer

Box 3: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Box 4: Enter your answer as an integer or decimal number. Examples: 3, -4, 5.5172
Enter DNE for Does Not Exist, oo for Infinity

Box 5: Select the best answer

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p 0.20

H_a : p > 0.20

= 0.21

n = 400

P₀ = 0.20

1 - P₀ = 0.80

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.21 - 0.20 / [(0.20 * 0.80) / 400]

= 0.500

P(z > 0.5) = 1 - P(z < 0.5) = 0.3085

P-value = 0.3085

= 0.005

P-value >

Fail to reject the null hypothesis .