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 0.0001Related Questions
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