Test the claim that the proportion of people who are confident is smaller than 90% at the 0.025 significance level.

MATLAB: An Introduction with Applications
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Author:Amos Gilat
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A well-known brokerage firm executive claimed that 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 600 people, 82% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is smaller than 90% at the 0.025 significance level.

The null and alternative hypothesis would be:

 

  • H0:p=0.9H0:p=0.9
    H1:p>0.9H1:p>0.9
  • H0:p=0.9H0:p=0.9
    H1:p≠0.9H1:p≠0.9
  • H0:μ≥0.9H0:μ≥0.9
    H1:μ<0.9H1:μ<0.9
  • H0:μ=0.9H0:μ=0.9
    H1:μ≠0.9H1:μ≠0.9
  • H0:μ≤0.9H0:μ≤0.9
    H1:μ>0.9H1:μ>0.9
  • H0:p=0.9H0:p=0.9
    H1:p<0.9H1:p<0.9



The test is:

 

 

left-tailed
right-tailed
two-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
A well-known brokerage firm executive claimed that 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 600 people, 82% of them said they are confident of meeting their goals.
Test the claim that the proportion of people who are confident is smaller than 90% at the 0.025 significance
level.
The null and alternative hypothesis would be:
O Ho:p = 0.9
H1:p > 0.9
O Ho:p = 0.9
H1:p + 0.9
O Ho: µ > 0.9
H1:µ < 0.9
0.9
%3D
H1:µ + 0.9
Ο Η: μ 0.9
H1:µ > 0.9
O Ho:p = 0.9
H1:p < 0.9
The test is:
left-tailed right-tailed two-tailed
The test statistic is:
(to 3 decimals)
The p-value is:
(to 4 decimals)
Based on this we:
O Reject the null hypothesis
O Fail to reject the null hypothesis
Transcribed Image Text:A well-known brokerage firm executive claimed that 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 600 people, 82% of them said they are confident of meeting their goals. Test the claim that the proportion of people who are confident is smaller than 90% at the 0.025 significance level. The null and alternative hypothesis would be: O Ho:p = 0.9 H1:p > 0.9 O Ho:p = 0.9 H1:p + 0.9 O Ho: µ > 0.9 H1:µ < 0.9 0.9 %3D H1:µ + 0.9 Ο Η: μ 0.9 H1:µ > 0.9 O Ho:p = 0.9 H1:p < 0.9 The test is: left-tailed right-tailed two-tailed The test statistic is: (to 3 decimals) The p-value is: (to 4 decimals) Based on this we: O Reject the null hypothesis O Fail to reject the null hypothesis
Expert Solution
Step 1

A well-known brokerage firm executive claimed that 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 600 people, 82% of them said they are confident of meeting their goals.

n = 600

p^  = 0.82

 claim:  proportion of people who are confident is smaller than 90% 

 significance level = 0.025

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