A well-known brokerage firm executive claimed that 10% of investors are currentl
ID: 2948570 • Letter: A
Question
A well-known brokerage firm executive claimed that 10% 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, 3% of them said they are confident of meeting their goals.
Test the claim that the proportion of people who are confident is smaller than 10% at the 0.01 significance level.
The null and alternative hypothesis would be:
H0:??0.1
H1:?>0.1
H0:p?0.1
H1:p>0.1
H0:p?0.1
H1:p<0.1
H0:?=0.1
H1:??0.1
H0:??0.1
H1:?<0.1
H0:p=0.1
H1:p?0.1
The test is:
right-tailed
two-tailed
left-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
Explanation / Answer
The statistical software output for this problem is:
One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.1
HA : p < 0.1
Hypothesis test results:
Hence,
Hypotheses:
H0:p?0.1
H1:p<0.1
Test statistic = -6.600
p - Value = 0.0000
Reject the null hypothesis
Proportion Count Total Sample Prop. Std. Err. Z-Stat P-value p 24 800 0.03 0.010606602 -6.5996633 <0.0001Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.