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ASSIGNMENT 4
DUE IN CLASS MONDAY, MARCH 25, 2019
INSTRUCTIONS:
I. Assignments are to be submitted in class prior to beginning of class on the due date.
II. For written questions, show all of your work. No credit will be given for answers without justification.
Do not use MINITAB for a question unless it specifically says to do so.
III. No late assignments will be accepted.
1. A federal agency responsible for enforcing laws concerning weights and measures routinely inspects
packages to determine whether the weight of the contents is at least as great as that advertised on the
package. A simple random sample of 25 observations of a product whose container claims that the net weight
is 10 ounces yielded a mean of 9.48 ounces and a variance of 1.43 ounces2
. Do these data provide sufficient
evidence to enable the agency to conclude that the true mean net weight is lower than the net weight
indicated on the container? Use ? = 0.05 . Give the conditions under which this test is valid.
2. A research manager at Coca-Cola claims that the true proportion, p, of cola drinkers that prefer CocaCola
over Pepsi is greater than 0.50. In a consumer taste test, 100 randomly selected people were given blind
samples of Coca-Cola and Pepsi. 58 of these subjects preferred Coca-Cola. Is there sufficient evidence at the
5% level of significance to validate Coca-Cola’s claim? Conduct an appropriate hypothesis test using (i) the
p-value method and (ii) the rejection point method.
3. A fast food company uses two management-training methods. Method 1 is a traditional method of training
and Method 2 is a supposedly new and innovative method. The company has just hired thirty-one (31) new
management trainees. Fifteen (15) of the trainees are randomly selected and assigned to Method 1 and the
remaining 16 trainees are assigned to Method 2. After three months of training, the management trainees
took a standardized test. The test was designed to evaluate their performance and learning from training. The
sample mean score and sample standard deviation of the two methods are given below. The management
wants to determine if the company should implement the new training method.
Conduct an appropriate hypothesis test at the 5% level of significance to determine if there is a difference in
the average score between the two methods. Conduct this test using (i) the p-value method, (ii) the critical
value method, and (iii) the confidence interval method. Give the conditions under which this test is valid.
Method x s
1 69 3.4
2 72 3.84. An experimental surgical procedure is being studied as an alternative to the old method. Both methods are
considered safe. Five surgeons perform the operation using both methods on two patients matched by age,
sex, and other relevant factors, with the time to complete the surgery (in minutes) recorded below.
Surgeon Old Method New Method
1 36 29
2 55 42
3 28 30
4 40 32
5 62 56
At the 1% level of significance, does the new method decrease the average length of the surgical procedure?
Give the conditions under which this test is valid.
5. The digital music players produced by a large Canadian manufacturer during the first two months of 2010
were of poor quality. A random sample of 100 players was obtained during this time and the players were
tested. It was determined that 25 of them were defective. As a result, quality control standards were then
tightened. A random sample of 100 players was taken during the next two months, 11 of which were
defective. Is there sufficient evidence to indicate that the new quality control standards were effective in
reducing the proportion of defective digital music players? To answer this question, conduct a hypothesis
test at the 5% level of significance.
6. MINITAB QUESTION. Hypothesis testing for when is known.
Imagine choosing n = 16 women at random from a large population and measuring their heights. Assume
that the heights of the women in this population are normally distributed with = 63.8 inches and = 3
inches. Suppose you then test the null hypothesis H0: = 63.8 versus the alternative that Ha : 63:8,
using = 0.10. Simulate the results of doing this test 100 times by entering the following commands:
MTB > random 16 c1-c100;
SUBC > normal 63.8 3.
MTB > ztest 63.8 3 c1-c100
(A) In how many of these hypothesis tests did you reject H0? In how many of these hypothesis tests did you
expect to reject H0?
(B) Are the p-values all the same for the 100 tests? Why or why not?
(C) Suppose you used = 0.01 instead of = 0.10. Does this change any of your decisions to reject or
not? In how many of these hypothesis tests did you expect to reject H0? In general, should the number of
rejections increase or decrease if = 0.01 is used instead of = 0.10?
(D) Now assume that the population really has a mean of = 63 instead of 63.8. Carry out the above 100
simulations again by changing the command “normal 63.8 3.” to “normal 63 3.” Once again, using = 0.10. In how many tests did you reject H0? In how many of these hypothesis tests did you expect to
reject H0?
(E) Is a rejection of H0 in part (A) a correct decision? If not, what type of error are you making in rejecting
H0?
(F) Is a rejection of H0 in part (D) a correct decision? If not, what type of error are you making in rejecting
H0?
ASSIGNMENT 4
DUE IN CLASS MONDAY, MARCH 25, 2019
INSTRUCTIONS:
I. Assignments are to be submitted in class prior to beginning of class on the due date.
II. For written questions, show all of your work. No credit will be given for answers without justification.
Do not use MINITAB for a question unless it specifically says to do so.
III. No late assignments will be accepted.
1. A federal agency responsible for enforcing laws concerning weights and measures routinely inspects
packages to determine whether the weight of the contents is at least as great as that advertised on the
package. A simple random sample of 25 observations of a product whose container claims that the net weight
is 10 ounces yielded a mean of 9.48 ounces and a variance of 1.43 ounces2
. Do these data provide sufficient
evidence to enable the agency to conclude that the true mean net weight is lower than the net weight
indicated on the container? Use ? = 0.05 . Give the conditions under which this test is valid.
2. A research manager at Coca-Cola claims that the true proportion, p, of cola drinkers that prefer CocaCola
over Pepsi is greater than 0.50. In a consumer taste test, 100 randomly selected people were given blind
samples of Coca-Cola and Pepsi. 58 of these subjects preferred Coca-Cola. Is there sufficient evidence at the
5% level of significance to validate Coca-Cola’s claim? Conduct an appropriate hypothesis test using (i) the
p-value method and (ii) the rejection point method.
3. A fast food company uses two management-training methods. Method 1 is a traditional method of training
and Method 2 is a supposedly new and innovative method. The company has just hired thirty-one (31) new
management trainees. Fifteen (15) of the trainees are randomly selected and assigned to Method 1 and the
remaining 16 trainees are assigned to Method 2. After three months of training, the management trainees
took a standardized test. The test was designed to evaluate their performance and learning from training. The
sample mean score and sample standard deviation of the two methods are given below. The management
wants to determine if the company should implement the new training method.
Conduct an appropriate hypothesis test at the 5% level of significance to determine if there is a difference in
the average score between the two methods. Conduct this test using (i) the p-value method, (ii) the critical
value method, and (iii) the confidence interval method. Give the conditions under which this test is valid.
Method x s
1 69 3.4
2 72 3.84. An experimental surgical procedure is being studied as an alternative to the old method. Both methods are
considered safe. Five surgeons perform the operation using both methods on two patients matched by age,
sex, and other relevant factors, with the time to complete the surgery (in minutes) recorded below.
Surgeon Old Method New Method
1 36 29
2 55 42
3 28 30
4 40 32
5 62 56
At the 1% level of significance, does the new method decrease the average length of the surgical procedure?
Give the conditions under which this test is valid.
5. The digital music players produced by a large Canadian manufacturer during the first two months of 2010
were of poor quality. A random sample of 100 players was obtained during this time and the players were
tested. It was determined that 25 of them were defective. As a result, quality control standards were then
tightened. A random sample of 100 players was taken during the next two months, 11 of which were
defective. Is there sufficient evidence to indicate that the new quality control standards were effective in
reducing the proportion of defective digital music players? To answer this question, conduct a hypothesis
test at the 5% level of significance.
6. MINITAB QUESTION. Hypothesis testing for when is known.
Imagine choosing n = 16 women at random from a large population and measuring their heights. Assume
that the heights of the women in this population are normally distributed with = 63.8 inches and = 3
inches. Suppose you then test the null hypothesis H0: = 63.8 versus the alternative that Ha : 63:8,
using = 0.10. Simulate the results of doing this test 100 times by entering the following commands:
MTB > random 16 c1-c100;
SUBC > normal 63.8 3.
MTB > ztest 63.8 3 c1-c100
(A) In how many of these hypothesis tests did you reject H0? In how many of these hypothesis tests did you
expect to reject H0?
(B) Are the p-values all the same for the 100 tests? Why or why not?
(C) Suppose you used = 0.01 instead of = 0.10. Does this change any of your decisions to reject or
not? In how many of these hypothesis tests did you expect to reject H0? In general, should the number of
rejections increase or decrease if = 0.01 is used instead of = 0.10?
(D) Now assume that the population really has a mean of = 63 instead of 63.8. Carry out the above 100
simulations again by changing the command “normal 63.8 3.” to “normal 63 3.” Once again, using = 0.10. In how many tests did you reject H0? In how many of these hypothesis tests did you expect to
reject H0?
(E) Is a rejection of H0 in part (A) a correct decision? If not, what type of error are you making in rejecting
H0?
(F) Is a rejection of H0 in part (D) a correct decision? If not, what type of error are you making in rejecting
H0?