(e) You wish to test the null hypothesis Họ: µz 244 mg/100 ml against the alternative HA: µ<244 mg/100 ml at the a = 0.05 level of significance. If the true population mean is as low as 219 mg/100 ml, you want to risk only a 5% chance of failing to reject Ho. How large a sample would be required? (f) How would the sample size change if you were willing to risk a 10% chance of failing to reject a false null hypothesis?
(e) You wish to test the null hypothesis Họ: µz 244 mg/100 ml against the alternative HA: µ<244 mg/100 ml at the a = 0.05 level of significance. If the true population mean is as low as 219 mg/100 ml, you want to risk only a 5% chance of failing to reject Ho. How large a sample would be required? (f) How would the sample size change if you were willing to risk a 10% chance of failing to reject a false null hypothesis?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 26PFA
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im having trouble with q 14 e and f.
![to completely eliminate the occurrence of type II errors? Explain.
14. Data from the Framingham Study allow us to compare the distributions of initial
serum cholesterol levels for two populations of males: those who go on to develop
coronary heart disease and those who do not. The mean serum cholesterol level of
the population of men who do not develop heart disease is µ = 219 mg/100 ml and
the standard deviation is o = 41 mg/100 ml [18]. Suppose, however, that you do
not know the true population mean; instead, you hypothesize that u is equal to
244. mg/100 ml. This is the mean initial serum cholesterol level of men who even-
tually develop the disease. Since it is believed that the mean serum cholesterol level
for the men who do not develop heart disease cannot be higher than the mean level
for men who do, a one-sided test conducted at the a = 0.05 level of significance is
appropriate.
(a) What is the probability of making a type I error?
(b) If a sample of size 25 is selected from the population of men who do not go
on to develop coronary heart disease, what is the probability of making a type
Il error?
(c) What is the power of the test?
(d) How could you increase the power?
(e) You wish to test the null hypothesis
Ho: µ 244 mg/100 ml
against the alternative
HA: µ<244 mg/100 ml
at the a = 0.05 level of significance. If the true population mean is as low as
219 mg/100 ml, you want to risk only a 5% chance of failing to reject Ho. How
large a sample would be required?
(f) How would the sample size change if you were willing to risk a 10% chance
of failing to reject a false null hypothesis?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe12869ed-f859-49f4-baa2-59815702973b%2F17d1401f-f082-496f-9a1f-e5b1a1676b4f%2F9qgbj4p_processed.png&w=3840&q=75)
Transcribed Image Text:to completely eliminate the occurrence of type II errors? Explain.
14. Data from the Framingham Study allow us to compare the distributions of initial
serum cholesterol levels for two populations of males: those who go on to develop
coronary heart disease and those who do not. The mean serum cholesterol level of
the population of men who do not develop heart disease is µ = 219 mg/100 ml and
the standard deviation is o = 41 mg/100 ml [18]. Suppose, however, that you do
not know the true population mean; instead, you hypothesize that u is equal to
244. mg/100 ml. This is the mean initial serum cholesterol level of men who even-
tually develop the disease. Since it is believed that the mean serum cholesterol level
for the men who do not develop heart disease cannot be higher than the mean level
for men who do, a one-sided test conducted at the a = 0.05 level of significance is
appropriate.
(a) What is the probability of making a type I error?
(b) If a sample of size 25 is selected from the population of men who do not go
on to develop coronary heart disease, what is the probability of making a type
Il error?
(c) What is the power of the test?
(d) How could you increase the power?
(e) You wish to test the null hypothesis
Ho: µ 244 mg/100 ml
against the alternative
HA: µ<244 mg/100 ml
at the a = 0.05 level of significance. If the true population mean is as low as
219 mg/100 ml, you want to risk only a 5% chance of failing to reject Ho. How
large a sample would be required?
(f) How would the sample size change if you were willing to risk a 10% chance
of failing to reject a false null hypothesis?
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