Answered: A well-known brokerage firm executive…

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter11: Data Analysis And Probability

Section: Chapter Questions

Problem 8CR

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Question

A well-known brokerage firm executive claimed that 80% 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 500 people, 75% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is smaller than 80% at the 0.10 significance level.

The null and alternative hypothesis would be:

H0:μ=0.8H0:μ=0.8
H1:μ≠0.8H1:μ≠0.8

H0:p≤0.8H0:p≤0.8
H1:p>0.8H1:p>0.8

H0:μ≤0.8H0:μ≤0.8
H1:μ>0.8H1:μ>0.8

H0:μ≥0.8H0:μ≥0.8
H1:μ<0.8H1:μ<0.8

H0:p≥0.8H0:p≥0.8
H1:p<0.8H1:p<0.8

H0:p=0.8H0:p=0.8
H1:p≠0.8H1:p≠0.8

The test is:

right-tailed

left-tailed

two-tailed

The test statistic is: (to 3 decimals)

The p-value is: (to 4 decimals)

Based on this we:

Fail to reject the null hypothesis
Reject the null hypothesis

Expert Solution

Step 1

$G i v e n, s a m p l e s i z e (n) = 500 s a m p l e p r o p o r t i o n (\hat{p}) = 0.75 p o p u l a t i o n p r o p o r t i o n (P) = 0.80 α = 0.10$