1. Periodically, Merrill Lynch customers are asked to evaluate Merrill Lynch financial consultants and services (2000 Merrill Lynch Client Satisfaction Survey). Higher ratings on the client satisfaction survey indicate better service with 7 the maximum service rating. Independent samples of service ratings for two financial consultants are summarized here. Consultant A has 10 years of experience, whereas consultant B has 1 year of experience. Use α = .05 and test to see whether the consultant with more experience has the higher population mean service rating.
Consultant A / Consultant Bn 1 = 16 / n 2 = 10
x 1 = 6.82 / x 2 = 6.25
s 1 = 0.7 / s 2 = 0.8
a. State the null and alternative hypotheses.
H0: μ1 - μ2
Selectgreater than 0greater than or equal to 0less than 0less than or equal to 0equal to 0not equal to 0Item 1
Ha: μ1 - μ2Selectgreater than 0greater than or equal to 0less than 0less than or equal to 0equal to 0not equal to 0Item 2
b. Compute the value of the test statistic (to 2 decimals).
Sp2 = [15(0.7)2+9(0.8)2]/24 = 0.54625
Sp = √0.54625 = 0.73909
Statistic = t = (6.82-6.25)/0.73909√(1/16+1/10) = 1.913 (df = 24)
Answer: 1.913
c.What is the p-value?
The p-value is Selectlessthan .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10between .10 and .20greater than .20Item 4
d. What is your conclusion?
SelectThe consultant with more experience has a higher population mean rating or Cannot conclude the consultant with more experience has a higher ratingItem 5
2.
A manufacturer produces both a deluxe and a standard model of an automatic sander designed for home use. Selling prices obtained from a sample of retail outlets follow.
Model Price ($) / Model Price ($)RetailOutlet / Deluxe / Standard / RetailOutlet / Deluxe / Standard
1 / 41 / 27 / 5 / 40 / 30
2 / 39 / 30 / 6 / 39 / 34
3 / 44 / 35 / 7 / 35 / 29
4 / 38 / 30
- The manufacturer's suggested retail prices for the two models show a $10 price differential. Use a .05 level of significance and test that the mean difference between the prices of the two models is $10.
Develop the null and alternative hypotheses.
H0 = μdSelectgreater than 10greater than or equal to 10equal to 10less than or equal to 10less than 10not equal to 10Item 1
Ha = μdSelectgreater than 10greater than or equal to 10equal to 10less than or equal to 10less than 10not equal to 10Item 2
b. Calculate the value of the test statistic (to 2 decimals).
Answer: -1.16
c. The p-value is Selectlessthan .01between .10 and .05between .05 and .10between .10 and .20between .20 and .40greater than .40Item 4
d. Can you conclude that the price differential is not equal to $10?
yes or no?
e. What is the 95% confidence interval for the difference between the mean prices of the two models (to 2 decimals)?
( 6.01,11.42 )
3. The Professional Golf Association (PGA) measured the putting accuracy of professional golfers playing on the PGA Tour and the best amateur golfers playing in the World Amateur Championship (Golf Magazine, January 2007). A sample of 1075 6-foot putts by professional golfers found 688 made puts. A sample of 1200 6-foot putts by amateur golfers found 696 made putts.
a.Estimate the proportion of made 6-foot putts by professional golfers. Estimate the proportion of made 6-foot putts by amateur golfers. (to 2 decimals)?.
Professional Golfers: p1 ¯Amateur Golfers: p2 ¯
Answers: p1-hat = 0.64 , p2-hat = 0.58
b. Which group had a better putting accuracy
SelectProfessional Golfers or Amateur GolfersItem3
c. What is the point estimate of the difference between the proportions of the two populations (to 2 decimals)?
Answer: 0.06
What does this estimate tell you about the percentage of putts made by the two groups of golfers?
SelectProfessional golfers make 6% more 6-foot putts than the very best amateur golfers or amateur golfers make 6% more 6-foot putts than the very best Professional golfersItem 5
d. What is the 95% confidence interval for the difference between the two population proportions? Interpret his confidence interval in terms of the percentage of putts made by the two groups of golfers (to 2 decimals).
(0.02 ,0.10 )
Interpretation: we are 95% confident that professional golfers make between 2% and 10% more6-foot putts than the very best amateur golfers
4. A 2003 New York Times/CBS News poll sampled 523 adults who were planning a vacation during the next six months and found that 141 were expecting to travel by airplane (New York Times News Service, March 2, 2003). A similar survey question in a May 1993 New York Times/CBS News poll found that of 477 adults who were planning a vacation in the next six months, 81 were expecting to travel by airplane.
a. State the hypotheses that can be used to determine whether a significant change occurred in the population proportion planning to travel by airplane over the 10-year-period.
Formulate the null and the alternative hypotheses.
H0: p1 - p2Selectgreater than or equal to 0greater than 0less than or equal to 0less than 0equal to 0not equal to 0Item 1
Ha: p1 - p2Selectgreater than or equal to 0greater than 0less than or equal to 0less than 0equal to 0not equal to 0Item 2
b. What is the sample proportion expecting to travel by airplane in 2003 (to 2 decimals)?
Answer: 0.27
What is the sample proportion expecting to travel by airplane in 1993 (to 2 decimals)?
Answer: 0.17
c. Use α = .01 and test for a significant difference.
What is the value of the test statistic (to 2 decimals)?
Answer: 3.79
Thep-value is Selectlessthan .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10between .10 and .20greater than .20Item 6.
Has a significant change occurred in the population proportion planning to travel by airplane over the 10-year period?
SelectYesNoItem 7
Which year appears to have a higher flying rate?
Select20031993Both years have the same rateItem 8
d. Based on the outcome of your hypothesis test, which of the following may be true?
SelectFlying was more expensive in 2003The population was more acceptable to flying on vacation in 1993 or Frequent flyer awards and discount fares made flying in 2003 economicalItem 9