Soal latihan review II bahan dr abis uts
1. A manufacturer of chocolate candies uses machines to package candies as they move along a filling
line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a
mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of
50 packages is selected periodically, and the packaging process is stopped if there is evidence that
the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50
packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051
ounce.
Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of
significance.)
2. The population mean waiting time to check out of a supermarket has been 10.73 minutes. Recently, in
an effort to reduce the waiting time, the supermarket has experimented with a system in which there
is a single waiting line with multiple checkout servers. A sample of 100 customers was selected, and
their mean waiting time to check out was 9.52 minutes, with a population standard deviation of 5.8
minutes.
a. At the 0.05 level of significance, using the critical value approach to hypothesis testing, is there
evidence that the population mean waiting time to check out is less than 10.73 minutes?
b. At the 0.05 level of significance, using the p-value approach to hypothesis testing, is there evidence
that the population mean waiting time to check out is less than 10.73 minutes?
c. Interpret the meaning of the p-value in this problem.
d. Compare your conclusions in (a) and (b)
3. The quality control manager at a water filter factory needs to estimate the mean life of a large
shipment of water filter. The standard deviation is 50 days. A random sample of 64 water filter
indicated a sample mean life of 86 days. Construct a 95% confidence interval estimate of the
population mean line of water filter in this shipment. Do you think that the manufacturer has the right
to state that the water filter last an average of 78 days? Explain.
4. A recent study (“Snack Ads Spur Children to Eat More,” The New York Times, July 20, 2009, p. B3)
found that children who watched a cartoon with food advertising ate, on average, 28.5 grams of
Goldfish crackers as compared to an average of 19.7 grams of Goldfish crackers for children who
watched a cartoon without food advertising. Although there were 118 children in the study, neither the
sample size in each group nor the sample standard deviations were reported. Suppose that there
were 59 children in each group, and the sample standard deviation for those children who watched
the food ad was 8.6 grams and the sample standard deviation for those children who did not watch
the food ad was 7.9 grams.
a. Assuming that the population variances are equal and α=0.05, is there evidence that the mean
amount of Goldfish crackers eaten was significantly higher for the children who watched food ads?
b. Assuming that the population variances are equal, construct a 95% confidence interval estimate of
the difference between the mean amount of Goldfish crackers eaten by the children who watched and
did not watch the food ad.
c. Compare the results of (a) and (b) and discuss.
5. Students in a business statistics course performed a completely randomized design to test the
strength of four brands of trash bags. One-pound weights were placed into a bag, one at a time, until
the bag broke. A total of 40 bags, 10 for each brand, were used. The data in give the weight (in
pounds) required to break the trash bags.
a. At the 0.05 level of significance, is there evidence of a difference in the mean strength of the four
brands of trash bags?
b. If appropriate, determine which brands differ in mean strength.
c. At the 0.05 level of significance, is there evidence of a difference in the variation in strength among
the four brands of trash bags?
d. Which brand(s) should you buy, and which brand(s) should you avoid? Explain.
6. Different age groups use different media sources for news. A study on this issue explored the use of
cell phones for accessing news. The study reported that 47% of users under age 50 and 15% of users
age 50 and over accessed news on their cell phones. (Data extracted from “Cellphone Users Who
Access News on Their Phones,” USA Today, March 1, 2010, p. 1A.) Suppose that the survey
consisted of 1,000 users under age 50, of whom 470 accessed news on their cell phones, and 891
users age 50 and over, of whom 134 accessed news on their cell phones.
a. Construct a 2 x 2 contingency table.
b. Is there evidence of a significant difference in the proportion that accessed the news on their cell
phones between users under age 50 and users 50 years and older? (Use α=0,05)
7. The marketing manager of a large supermarket chain has the business objective of using
shelf space most efficiently. Toward that goal, she would like to use shelf space to predict the sales of
pet food. Data is collected from a random sample of 12 equal-sized stores, with the following results:
Shelf Space
Weekly Sales
(X) (Feet)
(Y) ($)
1
5
160
2
5
220
3
5
140
4
10
190
5
10
240
6
10
260
7
15
230
8
15
270
9
15
280
10
20
260
11
20
290
12
20
310
13
25
320
14
25
350
15
25
380
a. Use least square method to determine the regression coefficient b0 and b1.
b. Interpret the meaning of the slope, in this problem.
c. Predict the weekly sales of pet food for stores with 9 feet of shelf space for pet food.
d. At 0.05 level of confidence, is there evidence of linear, is there a significant correlation
between shelf space and weekly sales?
Store
8. Do people of different age groups differ in their beliefs about response time to email messages? A
survey by the Center for the Digital Future of the University of Southern California reported that 70.7%
of users over 70 years of age believe that email messages should be answered quickly as compared
to 53.6% of users 12 to 50 years old. Suppose that the survey was based on 1,000 users over 70
years of age and 1,000 users 12 to 50 years old. At the 0.01 level of significance, is there evidence of
a significant difference between the two age groups in the proportion that believe that email
messages should be answered quickly?
line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a
mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of
50 packages is selected periodically, and the packaging process is stopped if there is evidence that
the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50
packages, the mean amount dispensed is 8.159 ounces, with a sample standard deviation of 0.051
ounce.
Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 0.05 level of
significance.)
2. The population mean waiting time to check out of a supermarket has been 10.73 minutes. Recently, in
an effort to reduce the waiting time, the supermarket has experimented with a system in which there
is a single waiting line with multiple checkout servers. A sample of 100 customers was selected, and
their mean waiting time to check out was 9.52 minutes, with a population standard deviation of 5.8
minutes.
a. At the 0.05 level of significance, using the critical value approach to hypothesis testing, is there
evidence that the population mean waiting time to check out is less than 10.73 minutes?
b. At the 0.05 level of significance, using the p-value approach to hypothesis testing, is there evidence
that the population mean waiting time to check out is less than 10.73 minutes?
c. Interpret the meaning of the p-value in this problem.
d. Compare your conclusions in (a) and (b)
3. The quality control manager at a water filter factory needs to estimate the mean life of a large
shipment of water filter. The standard deviation is 50 days. A random sample of 64 water filter
indicated a sample mean life of 86 days. Construct a 95% confidence interval estimate of the
population mean line of water filter in this shipment. Do you think that the manufacturer has the right
to state that the water filter last an average of 78 days? Explain.
4. A recent study (“Snack Ads Spur Children to Eat More,” The New York Times, July 20, 2009, p. B3)
found that children who watched a cartoon with food advertising ate, on average, 28.5 grams of
Goldfish crackers as compared to an average of 19.7 grams of Goldfish crackers for children who
watched a cartoon without food advertising. Although there were 118 children in the study, neither the
sample size in each group nor the sample standard deviations were reported. Suppose that there
were 59 children in each group, and the sample standard deviation for those children who watched
the food ad was 8.6 grams and the sample standard deviation for those children who did not watch
the food ad was 7.9 grams.
a. Assuming that the population variances are equal and α=0.05, is there evidence that the mean
amount of Goldfish crackers eaten was significantly higher for the children who watched food ads?
b. Assuming that the population variances are equal, construct a 95% confidence interval estimate of
the difference between the mean amount of Goldfish crackers eaten by the children who watched and
did not watch the food ad.
c. Compare the results of (a) and (b) and discuss.
5. Students in a business statistics course performed a completely randomized design to test the
strength of four brands of trash bags. One-pound weights were placed into a bag, one at a time, until
the bag broke. A total of 40 bags, 10 for each brand, were used. The data in give the weight (in
pounds) required to break the trash bags.
a. At the 0.05 level of significance, is there evidence of a difference in the mean strength of the four
brands of trash bags?
b. If appropriate, determine which brands differ in mean strength.
c. At the 0.05 level of significance, is there evidence of a difference in the variation in strength among
the four brands of trash bags?
d. Which brand(s) should you buy, and which brand(s) should you avoid? Explain.
6. Different age groups use different media sources for news. A study on this issue explored the use of
cell phones for accessing news. The study reported that 47% of users under age 50 and 15% of users
age 50 and over accessed news on their cell phones. (Data extracted from “Cellphone Users Who
Access News on Their Phones,” USA Today, March 1, 2010, p. 1A.) Suppose that the survey
consisted of 1,000 users under age 50, of whom 470 accessed news on their cell phones, and 891
users age 50 and over, of whom 134 accessed news on their cell phones.
a. Construct a 2 x 2 contingency table.
b. Is there evidence of a significant difference in the proportion that accessed the news on their cell
phones between users under age 50 and users 50 years and older? (Use α=0,05)
7. The marketing manager of a large supermarket chain has the business objective of using
shelf space most efficiently. Toward that goal, she would like to use shelf space to predict the sales of
pet food. Data is collected from a random sample of 12 equal-sized stores, with the following results:
Shelf Space
Weekly Sales
(X) (Feet)
(Y) ($)
1
5
160
2
5
220
3
5
140
4
10
190
5
10
240
6
10
260
7
15
230
8
15
270
9
15
280
10
20
260
11
20
290
12
20
310
13
25
320
14
25
350
15
25
380
a. Use least square method to determine the regression coefficient b0 and b1.
b. Interpret the meaning of the slope, in this problem.
c. Predict the weekly sales of pet food for stores with 9 feet of shelf space for pet food.
d. At 0.05 level of confidence, is there evidence of linear, is there a significant correlation
between shelf space and weekly sales?
Store
8. Do people of different age groups differ in their beliefs about response time to email messages? A
survey by the Center for the Digital Future of the University of Southern California reported that 70.7%
of users over 70 years of age believe that email messages should be answered quickly as compared
to 53.6% of users 12 to 50 years old. Suppose that the survey was based on 1,000 users over 70
years of age and 1,000 users 12 to 50 years old. At the 0.01 level of significance, is there evidence of
a significant difference between the two age groups in the proportion that believe that email
messages should be answered quickly?