Fundamentals of Statistics (5th Edition)
5th Edition
ISBN: 9780134508306
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 12.3, Problem 6AYU
a.
To determine
To find: The estimates of
b.
To determine
To compute: The standard error and the point estimate for
c.
To determine
The value of
s b 1
d.
To determine
To test:
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Question 17: 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 100 people, 81% 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 0.05 significance level.The null and alternative hypothesis would be:
H0:p≤0.9H0:p≤0.9H1:p>0.9H1:p>0.9
H0:μ≤0.9H0:μ≤0.9H1:μ>0.9H1:μ>0.9
H0:μ≥0.9H0:μ≥0.9H1:μ<0.9H1:μ<0.9
H0:μ=0.9H0:μ=0.9H1:μ≠0.9H1:μ≠0.9
H0:p=0.9H0:p=0.9H1:p≠0.9H1:p≠0.9
H0:p≥0.9H0:p≥0.9H1:p<0.9H1:p<0.9
The test is:
two-tailed
right-tailed
left-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
A random sample of n1=17�1=17 securities in Economy A produced mean returns of x̄ 1=5.6% x̄ 1=5.6% with s1=2.3%�1=2.3% while another random sample of n2=20�2=20 securities in Economy B produced mean returns of x̄ 2=4.6% x̄ 2=4.6% with s2=2.3%.�2=2.3%. At α =0.2 α =0.2, can we infer that the returns differ significantly between the two economies?
Assume that the samples are independent and randomly selected from normal populations with equal population variances ( σ 12= σ 22)( σ 12= σ 22).
T-Distribution Table
a. Calculate the test statistic.
t=�=
Round to three decimal places if necessary
b. Determine the critical value(s) for the hypothesis test.
+
Round to three decimal places if necessary
c. Conclude whether to reject the null hypothesis or not based on the test statistic.
Reject
Fail to Reject
Question 9
A well-known brokerage firm executive claimed that 60% 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 100 people, 61% of them said they are confident of meeting their goals.Test the claim that the proportion of people who are confident is larger than 60% at the 0.10 significance level.The null and alternative hypothesis would be:
H0:μ≤0.6H0:μ≤0.6H1:μ>0.6H1:μ>0.6
H0:p≥0.6H0:p≥0.6H1:p<0.6H1:p<0.6
H0:p≤0.6H0:p≤0.6H1:p>0.6H1:p>0.6
H0:μ≥0.6H0:μ≥0.6H1:μ<0.6H1:μ<0.6
H0:μ=0.6H0:μ=0.6H1:μ≠0.6H1:μ≠0.6
H0:p=0.6H0:p=0.6H1:p≠0.6H1:p≠0.6
The test is:
left-tailed
right-tailed
two-tailed
The test statistic is: (to 2 decimals)The p-value is: (to 4 decimals)Based on this we:
Fail to reject the null hypothesis
Reject the null hypothesis
Chapter 12 Solutions
Fundamentals of Statistics (5th Edition)
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