In the past, 20% of applicants for admission into a master's program had GRE scores above 650. Of the 88 students applying to be admitted into the program in 1981, 22 had GRE scores above 650. Do the 1981 applicants have greater GRE scores than previous applicants at the 5% level of significance? Ans. No

MATLAB: An Introduction with Applications
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5.39
5.40
-41 (4
5.42
5.43
5.44
In the past, 20% of applicants for admission into a master's program had GRE scores above 650. Of the 88
students applying to be admitted into the program in 1981, 22 had GRE scores above 650. Do the 1981
applicants have greater GRE scores than previous applicants at the 5% level of significance?
Ans. No
5.45
Find the probability of accepting Ho (that = 650) for Prob. 5.39 if = 0.043 and
(b) p = 0.22, (c) p = 0.24, (d) p = 0.25, (e) p = 0.26, and () p = 0.28.
(c) 0.591 (d) 0.5 (e) 0.409 () 0.242
Ans. (a) 0.877 (b) 0.758
(a) p = 0.20,
(a) What is the value of a when p = 0.20 in Prob. 5.39 (b) How can the OC curve be derived for Prob. 5.39?
Ans. (a) 0.123 (b) By joining the value of 1-a for p = 0.20 with the values of ß found in Prob. 5.40(b) to
(f) for various values of p > 0.20
Find the probability of rejecting Ho (that = 650) for Prob. 5.39 if o = 0.043 and (a) p = 0.20,
(b) p = 0.22, (c) p = 0.24, (d) p = 0.25, (e) p = 0.26, and (f) p = 0.28.
Ans. (a) 0.123 (b) 0.242 (c) 0.409 (d) 0.5 (e) 0.591 () 0.758
TESTING HYPOTHESES FOR DIFFERENCES BETWEEN TWO MEANS OR PROPORTIONS
A consulting firm wants to decide at the 5% level of significance if the salaries of construction workers differ
between New York and Chicago. A random sample of 100 construction workers in New York has an
average weekly salary of $400 with a standard deviation of $100. In Chicago, a random sample of 75
workers has an average weekly salary of $375 with a standard deviation of $80. Is there a significant
difference between the salaries of construction workers in New York and Chicago at (a) The 5% level?
(b) The 10% level?
Ans. (a) No (b) Yes
How can we get the power curve for Prob. 5.39?
Ans. By joining the values found in Prob. 5.42(a) to (f) for various alternative values of p > 0.2.
A random sample of 21 AFC football players has a mean weight of 265 lb with a standard deviation of 30 lb,
while a random sample of 11 NFC players has a mean weight of 240 lb with a standard deviation of 20lb. Is
the mean weight of all AFC football players greater than that for the NFC players at the 1% level of
significance?
Ans. Yes
Transcribed Image Text:5.39 5.40 -41 (4 5.42 5.43 5.44 In the past, 20% of applicants for admission into a master's program had GRE scores above 650. Of the 88 students applying to be admitted into the program in 1981, 22 had GRE scores above 650. Do the 1981 applicants have greater GRE scores than previous applicants at the 5% level of significance? Ans. No 5.45 Find the probability of accepting Ho (that = 650) for Prob. 5.39 if = 0.043 and (b) p = 0.22, (c) p = 0.24, (d) p = 0.25, (e) p = 0.26, and () p = 0.28. (c) 0.591 (d) 0.5 (e) 0.409 () 0.242 Ans. (a) 0.877 (b) 0.758 (a) p = 0.20, (a) What is the value of a when p = 0.20 in Prob. 5.39 (b) How can the OC curve be derived for Prob. 5.39? Ans. (a) 0.123 (b) By joining the value of 1-a for p = 0.20 with the values of ß found in Prob. 5.40(b) to (f) for various values of p > 0.20 Find the probability of rejecting Ho (that = 650) for Prob. 5.39 if o = 0.043 and (a) p = 0.20, (b) p = 0.22, (c) p = 0.24, (d) p = 0.25, (e) p = 0.26, and (f) p = 0.28. Ans. (a) 0.123 (b) 0.242 (c) 0.409 (d) 0.5 (e) 0.591 () 0.758 TESTING HYPOTHESES FOR DIFFERENCES BETWEEN TWO MEANS OR PROPORTIONS A consulting firm wants to decide at the 5% level of significance if the salaries of construction workers differ between New York and Chicago. A random sample of 100 construction workers in New York has an average weekly salary of $400 with a standard deviation of $100. In Chicago, a random sample of 75 workers has an average weekly salary of $375 with a standard deviation of $80. Is there a significant difference between the salaries of construction workers in New York and Chicago at (a) The 5% level? (b) The 10% level? Ans. (a) No (b) Yes How can we get the power curve for Prob. 5.39? Ans. By joining the values found in Prob. 5.42(a) to (f) for various alternative values of p > 0.2. A random sample of 21 AFC football players has a mean weight of 265 lb with a standard deviation of 30 lb, while a random sample of 11 NFC players has a mean weight of 240 lb with a standard deviation of 20lb. Is the mean weight of all AFC football players greater than that for the NFC players at the 1% level of significance? Ans. Yes
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