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9. A well-known brokerage firm executive claimed that 30% of investors are curre

ID: 3351743 • Letter: 9

Question

9. A well-known brokerage firm executive claimed that 30% 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, 36% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is larger than 30% at the 0.01 significance level.

The null and alternative hypothesis would be:

A H0:p=0.3H0:p=0.3
H1:p0.3H1:p0.3

B H0:0.3H0:0.3
H1:>0.3H1:>0.3

C H0:p0.3H0:p0.3
H1:p<0.3H1:p<0.3

D H0:p0.3H0:p0.3
H1:p>0.3H1:p>0.3

E H0:0.3H0:0.3
H1:<0.3H1:<0.3

F H0:=0.3H0:=0.3
H1:0.3H1:0.3



The test is:

A two-tailed

B left-tailed

C right-tailed



The test statistic is:  (to 3 decimals)

The p-value is:  (to 4 decimals)

Based on this we:

A Reject the null hypothesis

B Fail to reject the null hypothesis

Explanation / Answer

The statistical software output for this problem is:

One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.3
HA : p > 0.3

Hypothesis test results:

Hence,

Hypotheses:

H0: p 0.3
H1: p > 0.3

Option D is correct.

The test is right - tailed. Option C is correct.

Test statistic = 3.703

P - value = 0.0001

Reject the null hypothesis

Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 288 800 0.36 0.016201852 3.7032804 0.0001