A psychologist is studying smokers' self-images, which she measures using the self-image (SI) score from a personality inventory. She would like to examine the mean SI score u for the population of all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is 85 and that the standard deviation is 12, but the psychologist has good reason to believe that the value for the mean has decreased. She decides to perform a statistical test and chooses a random sample of 75 smokers' SI scores. She'll use the value 12 for the population standard deviation, and she'll test at the 0.05 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) (a) What are the null hypothesis H, and the alternative hypothesis H, that the psychologist should use for the test? Họ: 0 H1: 0 믐 D=0 Oso (b) Assuming that the actual value of u is 82, what is the probability that the psychologist commits a Type Il error? Round your response to two or more decimal places. (c) What is the probability that the psychologist commits a Type I error? Round your response to two or more decimal places.
A psychologist is studying smokers' self-images, which she measures using the self-image (SI) score from a personality inventory. She would like to examine the mean SI score u for the population of all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is 85 and that the standard deviation is 12, but the psychologist has good reason to believe that the value for the mean has decreased. She decides to perform a statistical test and chooses a random sample of 75 smokers' SI scores. She'll use the value 12 for the population standard deviation, and she'll test at the 0.05 level of significance. Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal places, and round your responses as indicated. (If necessary, consult a list of formulas.) (a) What are the null hypothesis H, and the alternative hypothesis H, that the psychologist should use for the test? Họ: 0 H1: 0 믐 D=0 Oso (b) Assuming that the actual value of u is 82, what is the probability that the psychologist commits a Type Il error? Round your response to two or more decimal places. (c) What is the probability that the psychologist commits a Type I error? Round your response to two or more decimal places.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Transcribed Image Text:A psychologist is studying smokers' self-images, which she measures using the self-image (SI) score from a personality
inventory. She would like to examine the mean SI score u for the population of all smokers. Previously published studies
have indicated that the mean SI score for the population of all smokers is 85 and that the standard deviation is 12, but the
psychologist has good reason to believe that the value for the mean has decreased.
She decides to perform a statistical test and chooses a random sample of 75 smokers' SI scores. She'll use the value 12 for
the population standard deviation, and she'll test at the 0.05 level of significance.
Based on this information, answer the questions below. Carry your intermediate computations to four or more decimal
places, and round your responses as indicated.
(If necessary, consult a list of formulas.)
(a) What are the null hypothesis H, and the alternative hypothesis
H, that the psychologist should use for the test?
Ho: 0
H1: 0
O=0
OSO
O20
(b) Assuming that the actual value of u is 82, what is the
probability that the psychologist commits a Type Il error?
Round your response to two or more decimal places.
(c) What is the probability that the psychologist commits a Type I
error? Round your response to two or more decimal places.
(d) Suppose that the psychologist decides to perform another
statistical test using the same population, the same null and
alternative hypotheses, and the same level of significance, but
for this second test the psychologist chooses a random sample
of size 50 instead of a random sample of size 75. Assuming that
the actual value of u is 82, how does the power of this second
test compare to the power of the original test?
OThe power of the second test is greater than the power of the
original test
The power of the second test is less than the power of the
original test
The powers of the two tests are equal
olo
Ix
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