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The American Association of Individual Investors conducts a weekly survey of its members to measure the percent who are bullish, bearish, and neutral on the stock market for the next six months. For the week ending November 7, 2012, the survey results showed 38.5% bullish, 21.6% neutral, and 39.9% bearish (AAII website, November 12, 2012). Assume these results are based on a sample of 300 AAII members. a. Over the long term, the proportion of bullish AAII members is .39. Conduct a hypothesis test at the 5% level of significance to see if the current sample results show that bullish sentiment differs from its long term average of .39. What are your findings? b. Over the long term, the proportion of bearish AAII members is .30. Conduct a hypothesis test at the 1% level of significance to see if the current sample results show that bearish sentiment is above its long term average of .30. What are your findings? c. Would you feel comfortable extending these results to all investors? Why or why not?

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STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

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BuyFindarrow_forward

STATISTICS F/BUSINESS+ECONOMICS-TE...

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884
Chapter 9.5, Problem 45E
Textbook Problem
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The American Association of Individual Investors conducts a weekly survey of its members to measure the percent who are bullish, bearish, and neutral on the stock market for the next six months. For the week ending November 7, 2012, the survey results showed 38.5% bullish, 21.6% neutral, and 39.9% bearish (AAII website, November 12, 2012). Assume these results are based on a sample of 300 AAII members.

  1. a. Over the long term, the proportion of bullish AAII members is .39. Conduct a hypothesis test at the 5% level of significance to see if the current sample results show that bullish sentiment differs from its long term average of .39. What are your findings?
  2. b. Over the long term, the proportion of bearish AAII members is .30. Conduct a hypothesis test at the 1% level of significance to see if the current sample results show that bearish sentiment is above its long term average of .30. What are your findings?
  3. c. Would you feel comfortable extending these results to all investors? Why or why not?

a.

To determine

Check whether the bullish sentiment differs from its long-term average of 0.39.

Explanation of Solution

Calculation:

The given information is that n=300, p¯=0.385, and x=116(=38.5% of 300).

Here, the claim is that the bullish sentiment differs from its long-term average of 0.39. This can be written as p0.39. The complement of the claim is p=0.39. In the given experiment, the alternative hypothesis indicates the claim.

The null and alternative hypotheses are given below:

Null hypothesis:

H0:p=0.39

Alternative hypothesis:

Ha:p0.39 (claim)

p-value:

Software Procedure:

A step-by-step procedure to obtain the p-value using MINITAB software:

  • Choose Stat > Basic Statistics > 1 Proportion.
  • Choose Summarized data

b.

To determine

Check whether the proportion of bearish AAII members is greater than 0.30.

c.

To determine

Check whether extending the results to all investors is comfortable or not.

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Chapter 9 Solutions

STATISTICS F/BUSINESS+ECONOMICS-TEXT
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