- A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 40 subscribers to plan A is $ 57,000 with a standard deviation of $ 9,200. This distribution is positively skewed, the actual coeffiecient of skewness is 2.11. For a sample of 30 subscribers to plan B mean income is $ 61,000 with a standard deviation os $ 7,100. The distribustion of subscribers is also positively skewed but not as severly. The coefficient is 1.54. At the 0.05 significance level, is it reasonable to conclude the mean income of those selecting plan B is larger? What is the p value? Do the coefficient of skewness affect the results of the hypotheseis test ? Why? Two sample test of hypothesis no 1

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 393, number 31)*

*2. *A computer manufacturer offers a help line that purchasers can call for help 24 hours a day, 7 days a week. Clearing these calls for help in timely fashion is important to the company’s image. After testing the caller that resolution of the problem is important the caller is asked whether the issue is sofrware or hardware related. The mean time it takes a technician to resolve a software issue is 18 minutes with a standard deviation of 4.2 minutes. This information was obtained from a smple of 35 monitored calls. For a study of 45 hardware issues, the mean time for the technician to resolve the problem was 15.5 minutes with a standard deviation of 3.9 minutes. This information was also obtained from monitores calls. At the 0.05 significance level does it take longer to resolve software issue? What is tha p value? Two sample test of hypothesis no 2

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 393, number 32)*

3. Supppose the manufacture of Advil, a common headache remedy, recently developed a new formulation of the drugn that is claimed to be more effective. To evaluate the new drug, a sample of 200 current users is asked to try it. After a one month trial, 180 indicated the new drug was more effective in relieving a headache. At the same time a sample of 300 Advil users is given the current drug but told it is the new formulation. From this group, 261 said it was an improvement. At 0.05 significance level can we conclude that the drug is more effective Two sample test of hypothesis no 3

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 393, number 33)*

4. Business, particularly those in the food preparation industry such as general Mills, Kellog and Betty Crocker regularly use coupons as a brand allegiance bulder yo stimulate their retailing. There is uneasiness that the users of paper coupons are different from the users of e-coupons (coupons disseminated by means of internet). One survey recorded the age of each person who redeemed a coupon with the type (either electronic or paper). The sample of 35 e-coupon used had a mean age of 33.6 years with a standard deviation of 10.9, while a similar sample of 25 traditional paper coupon clippers had a mean age of 39.5 with a standard deviation of 4.8. assume the population standard deviations are not the same. Using a significance of 0.01, test the hypothesis of no difference ages of the two groups of coupon clients. Two sample test of hypothesis no 4

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 394, number 42*

5. Grand Strand Family Medical Centre is specifically set up to treat minor medical emergencies for visitors to the Myrtle area. There are two facilities, one in the Little river area and the other in Murrells inlet. The quality assurance Departmenet wishes to compare the mean waiting time for the patients at the two locations. Samples of the waiting times, reported in minutes. Assume the population standard deviations are not the same. At the 0.05 significance level is there a difference in the mean waiting time? Two sample test of hypothesis no 5

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 395, number 46) *

6. Commercial Bank and Trust company is studying the use of its automatic teller machines (ATMs). Of particular ineterse is whether young adults 9under 25 years) use the machines more than the senior citizens. To investigate further, samples of customers under 25 years of age and customer over 60 years of age were selected. The number of ATM transaction last month was determined for each selected individual and the results are shown below. At the 0.01 sugnificance level, can bank management conclude that younger customers use ATMs more? Two sample test of hypothesis no 6

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 395, number 47) *

7. Two boats, the Prada (Italy) and the Oracle (USA) are competing for a pot in the upcoming America’s Cup Race. The race over a part of the course several times. Below are the sample times in minutes. Assume the population standard deviations are not the same. At the 0.05 significance level, can we conclude that there is a different in their mean times ? Two sample test of hypothesis no 7

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 395, number 48) *

8. The manufacturer of an MP3 player wanted to know whether a 10 percent reduction in price is enough to increase the sales of its product. To investigate, the owner randomly selected eight outlets and sold the MP3 player at the reduced price. At seven randomly selected outlets, the MP# player was sold at the regular price. Reported below si the number of units sold last month at the sampled outlets. At the 0.01 siginificance level, can the manufacturer conclude that the price reduction resulted in an increase in sales? Two sample test of hypothesis no 8

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 395, number 49) *

*9. *One of the music industry’s most pressing questions os : Can paid download stores content nose to nose with free peer to peer download servces ? data gathered over the last 12 months show Apple’s I tunes was used by an averageof 1.65 million families with a sample deviation of 0.56 million family units. Over the same 12 montoh WinMX (a no cost P2P download service) was used by an average 2.2 million families with a sample standard deviation of 0.30 million. Assume the population standar deviation are not the same. Using a significance level of 0.05, test hypotheses of no difference in the mean number of household picking either variety of service to download songs. Two sample test of hypothesis no 9

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 394, number 41*

10. Businesses, particularry those in the food preparation industry such as general Miils, Kellog and Betty Crocke regularly use coupons as brand allegiance builder to stimulate theor retailing. There is uneasiness that the users of paper coupons are different from the users of e-coupons (coupons disseminated by menas of internet). One survey recorded the age of each person who redeemed a coupon along with the type (either electronic or paper). The sample of 35 e-coupon users had a mean age of 33.6 years with a standard deviation of 10.9, while similar sample of 25 traditional paper-coupon clipper had a mean age of 39.5 with a standard deviation of 4.8 . Assume the population standard deviation are not the same. Using a significance level of 0.01, test the hypothesis of no difference in the mean age of the two groups of coupon client Two sample test of hypothesis no 10

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 394, number 42)*

11. A number of minor automobile accidents occur at various high risk intersections in Teton County despite traffic lights. The traffic department claims that a modification in the type of ligh will reduce these accidents. The county commissioners have agreed to a proposed experiment. Eight intersections were chosen at random, and the lights at those intersections were modified. The number of minor accidents during a six month period before and after modifications were :At the 0.01 siginificance level is it reasonable to conclude that the modification reduced the number of traffic accidentsTwo sample test of hypothesis no 11

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 396, number 50)
*

12. The following data on annual rates of return were collected from five stocks listed on New York Exchange (The big board) anf five stocks listed in NASDAQ. Assume the population standard deviation are the same. At the 0.10 significance level, can we conclude that the annual rates of return are higher on the big board? *(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 397, number 56) Two sample test of hypothesis no 12
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13.A coffe manufacturer is interested in whether the mean daily consumption of regular coffe drinkers is less than that of decaffeinated drinkers. Assume the population standard deviation for those drinking regular coffe is 1.20 cups per day and 1.36 cups per day for those drinking the decaffeinated coffe. A random sample of 50 reguler coffee drinkers showed a mean of 4.35 cups per day. A sample of 40 decaffeinated coffe drinkers showed a mean of 5.84 perday. Use the 0.01 significance level.. Compute the p value

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 393, number 30) Two sample test of hypothesis no 13*

14. Each month the National Association of Purchasing Managers published the NAPM Index. One of the question asked on survey to purchasing agents is : Do you the economy is contracting ? Last month, of the 360 responses, 160 answered ye to the question. This month 170 of the 290 responses indicated that they felt the economy was contracting. At the 0.05 significance level, can we conclude that a larger proportion of the agents believe the economy is contracting this month?

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 394, number 34) Two sample test of hypothesis no 14*

15. There are two major internet providers in the Colorado springs, Colorado area, one called HTC and the other Mountain Communication. We want to investigate whether there is a different in the proportion of times a customer is able to access the internet. During a one week period, 500 calls were placed at random times throughout the day and night to HTC. A connection was made to the internet on 450 occasions. A similar one week study with Mountain Communications showed the internet to be available on 352 of 400 trials. At the 0.01 significant level, is there a difference in the percent of time that aaccess to the internet is successful?

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 394, number 36) Two sample test of hypothesis no 15
*

16. Grand strand family Medical Centre is specifically set up to treat minor medical emergencies for visitors to the Myrtie Beach area. Thera are two facilities, one in the Little river Area and the other in Murrells inlet. The quality assurance Departement wishes to compare the mean waiting for patients at two locations. Samples of the waiting times, reported in minutes, follow…Assume the population standard deviations are not the same. At the 0.05 significance level, is there a difference in the mean waiting time ?

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 395, number 46 Two sample test of hypothesis no 16
*

17. A number of minor automobile accident occur at various high risk intersections in Teton county despite traffic light. The traffic department claims that a modification in the type of light will reduce these eccidents. The county commissioners have agreed to a proposed experiment. Eight intersection were chosen at random and the lights at those intersections were modified. The number of minor accidents during a six month period berfoe and after the modification were …At the 0.01 significance level is it reasonable to conclude that the modification reduce the number of traffic accidents ?

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 396, number 50) Two sample test of hypothesis no 17*

18. The president of the American Insurance Institute wants to compare the yearly costs of auoto insurance offered by two leading companies. He selects a sample of 15 families, some with only a single insured dricer, others with several teenage drivers and pays each family a stipend to contact the two companies and ask for a proce quote. To make the data comparable, certain features, such as a deductible amount and limits of liability are standardized. The sample information is reported below. At the 0.10 significance level, can we conclude that there is a difference in the amount quoted ?

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 396, number 52 Two sample test of hypothesis no 18
*

19. The following data resulted from a taste test of two different chocolate bars. The pisrt number is rating of the taste, which could range from 0 to 5, with a 5 indicating the person liked the taste. The second number indicate whether a “secrect ingeridient” was presnt. If the ingredient was present a code of 1 was used and 0 otherwise. Assume the population standard deviation are the same. At the 0.05 significance level, do these data show a difference in the taste ratings?

*(Lind, Marchal, Wathen., Statistical Technique in Business and Economics., Fourteenth Edition., McGraw-Hill., page 397, number54) Two sample test of hypothesis no 19*

20. In manufacturing, does worker productivity drop on Friday? In en effort to determine whether it does, a company’s personnel analyst randomly selects from a manufacturing plant five workers who make the same part. He measures their ouput on Wednesday and again on Friday and obtain the following results.

Worker |
Wednesday ouput |
Friday output |

1 |
71 |
53 |

2 |
56 |
47 |

3 |
75 |
52 |

4 |
68 |
55 |

5 |
74 |
58 |

The analyst use and assume the difference in productivity is normally distributed.

(a) Does (a) worker productivity drop on Friday (b) If the The Maximum productivity drop error is 2 days, do samples provide enough evidence to show that productivity drops on Friday ? Two sample test of hypothesis no 20

21. One of the most important aspects of a store’s image is perceived quality of its merchandise. Suppose image perception of shoppers of speciality stores and shoppers of discount stores are being compared. A random sample of shoppers is taken at each type of store, and the shoppers are asked whether the quality of merchandise is a determining factor in their perception of the store’s image. Some 75 % of 350 shoppers at the specaility store say YES, but only 52% of the 500 shoppers at the discount store say YES. Use these data to determine if there is a significance difference between the proportion of shoppers at speciality stores and the proportion of shoppers at discount stores who say that quality of merchandise is a determining factor in their perception of store’s image. Use Two sample test of hypothesis no 21