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 50% 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 400 people, 51% of them said they are confident of meeting their goals.

Test the claim that the proportion of people who are confident is larger than 50% at the 0.05 significance level.

The null and alternative hypothesis would be:

H0:μ=0.5H0:μ=0.5
H1:μ≠0.5H1:μ≠0.5

H0:p≥0.5H0:p≥0.5
H1:p<0.5H1:p<0.5

H0:μ≥0.5H0:μ≥0.5
H1:μ<0.5H1:μ<0.5

H0:p=0.5H0:p=0.5
H1:p≠0.5H1:p≠0.5

H0:μ≤0.5H0:μ≤0.5
H1:μ>0.5H1:μ>0.5

H0:p≤0.5H0:p≤0.5
H1:p>0.5H1:p>0.5

The test is:

two-tailed

left-tailed

right-tailed

The test statistic is: (to 3 decimals)

The p-value is: (to 4 decimals)

Based on this we: