In: Statistics and Probability
A well-known brokerage firm executive claimed that at least 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, 88% of them said they are confident of meeting their goals.
1. If you were a broker for this well know brokerage firm which significance level do you want the statistician to use and why? (Answer as a complete sentence)
2. If you were an investor shopping investment firms which significance level do you want the statistician to use and why? (Answer as a complete sentence) Please and thank you!!!
(1)
If we were a broker for this well known brokerage firm we want the statistician to use the significance level
= 0.01
Reason:
H0: Null Hypothesis: P 0.90 (Claim)
HA: Alternative Hypothesis: P < 0.90
n = 800
p = Sample Proportion= 0.88
P = Population Proportion = 0.90
Q = 1 - P = 0.10
SE =
Test statistic is:
Z = (0.88 - 0.90)/0.0106 = - 1.89
One Tail - Left side Test
If we take = 0.01,
critical value of Z = - 2.33
Since the calculated value of Z = - 1.89 is greater than critical value of Z = - 2.33 the difference is not significant. Fail to reject Null hypothesis.
Conclusion:
The data support the claim that at least 90% of the investors are correctly confident of meeting their investment goals.
Since conclusion that at least 90% of the investors are correctly confident of meeting their investment goals will satisfy the executive, we want the statistician to use the significance level = 0.01.
(2)
If we were an investor shopping investment firms, we want the statistician to use the significance level
= 0.05
Reason
If we take = 0.05,
critical value of Z = - 1.645
Since the calculated value of Z = - 1.89 is less than critical value of Z = - 1.645, the difference is significant. Reject Null hypothesis.
Conclusion:
The data do not support the claim that at least 90% of the investors are correctly confident of meeting their investment goals.
Since conclusion that at least 90% of the investors are not correctly confident of meeting their investment goals will make the executive to make actions on improving the investors in meeting their goals, , we want the statistician to use the significance level = 0.05.