Question

In: Statistics and Probability

A well-known brokerage firm executive claimed that at least 90% of investors are currently confident of...

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!!!

Solutions

Expert Solution

(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.


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