Socially conscious investors screen out stocks of alcohol and tobacco makers, firms with poor environmental records, and companies with poor labor practices. Some examples of "good," socially conscious companies are Johnson and Johnson, Dell Computers, Bank of America, and Home Depot. The question is, are such stocks overpriced? One measure of value is the P/E, or price-to-earnings ratio. High P/E ratios may indicate a stock is overpriced. For the S&P Stock Index of all major stocks, the mean P/E ratio is μ = 19.4. A random sample of 31 "socially conscious" stocks gave a P/E ratio sample mean of x = 18.3, with sample standard deviation s = 4.2. At a 10% level of significance does this indicate that the mean P/E ratio of all socially conscious stocks is different (either way) from the mean P/E ratio of the S&P Stock Index? What distribution will be used for this test? Student's t Is this test right-tailed, left-tailed, or two-tailed? two-tailed Using the critical region method which curve represents this test: c (b) H₁: μ>k Right-tailed (c) H₂: k Two-tailed (a) H₁:

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.2: Representing Data
Problem 22PFA
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Socially conscious investors screen out stocks of alcohol and tobacco makers, firms with poor environmental records, and companies with poor labor practices. Some
examples of "good," socially conscious companies are Johnson and Johnson, Dell Computers, Bank of America, and Home Depot. The question is, are such stocks
overpriced? One measure of value is the P/E, or price-to-earnings ratio. High P/E ratios may indicate a stock is overpriced. For the S&P Stock Index of all major stocks,
the mean P/E ratio is u 19.4. A random sample of 31 "socially conscious" stocks gave a P/E ratio sample mean of x 18.3, with sample standard deviation s = 4.2.
At a 10% level of significance does this indicate that the mean P/E ratio of all socially conscious stocks is different (either way) from the mean P/E ratio of the S&P Stock
Index?
=
=
What distribution will be used for this test? Student's t
Is this test right-tailed, left-tailed, or two-tailed? two-tailed
Using the critical region method which curve represents this test: c
(c) H₁: k
(b) Η: μ > Κ
Right-tailed
Two-tailed
(a) H₁: <k
Left-tailed
Area = a
k
Critical region
What is the critical value for this test?
k
Area
Calculate the sample test statistic:
Will you reject or fail to reject the null hypothesis?
State your conclusion by filling in the blanks:
At
α
Critical region
Area = a/2
k
Critical regions
(three decimal places)
Area = a/2
% level of significance, (reject or fail to reject)
the null hypothesis. There is (sufficient or insufficient)
evidence to say that the mean P/E ratio of all socially conscious stocks is different from the mean P/E ratio of the S&P Stock Index.
Transcribed Image Text:Socially conscious investors screen out stocks of alcohol and tobacco makers, firms with poor environmental records, and companies with poor labor practices. Some examples of "good," socially conscious companies are Johnson and Johnson, Dell Computers, Bank of America, and Home Depot. The question is, are such stocks overpriced? One measure of value is the P/E, or price-to-earnings ratio. High P/E ratios may indicate a stock is overpriced. For the S&P Stock Index of all major stocks, the mean P/E ratio is u 19.4. A random sample of 31 "socially conscious" stocks gave a P/E ratio sample mean of x 18.3, with sample standard deviation s = 4.2. At a 10% level of significance does this indicate that the mean P/E ratio of all socially conscious stocks is different (either way) from the mean P/E ratio of the S&P Stock Index? = = What distribution will be used for this test? Student's t Is this test right-tailed, left-tailed, or two-tailed? two-tailed Using the critical region method which curve represents this test: c (c) H₁: k (b) Η: μ > Κ Right-tailed Two-tailed (a) H₁: <k Left-tailed Area = a k Critical region What is the critical value for this test? k Area Calculate the sample test statistic: Will you reject or fail to reject the null hypothesis? State your conclusion by filling in the blanks: At α Critical region Area = a/2 k Critical regions (three decimal places) Area = a/2 % level of significance, (reject or fail to reject) the null hypothesis. There is (sufficient or insufficient) evidence to say that the mean P/E ratio of all socially conscious stocks is different from the mean P/E ratio of the S&P Stock Index.
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