08 Oct Small calculators are assembled on a production line. A supervisor is interested in studying the production rate on one part of the line to see how the number of items produced by a worker varies as a function of the time spent on the line.

Small calculators are assembled on a production line.  A supervisor is interested in studying the production rate on one part of the line to see how the number of items produced by a worker varies as a function of the time spent on the line.  Six workers are randomly selected for observation and the number of pieces completed is noted for each after a predetermined length of time has elapsed. 

 

Time Spent on Production Line (min.)

 

15

 

22

 

28

 

23

 

30

 

20

 

Number of Units Assembled

 

1

 

3

 

5

 

4

 

5

 

3

 

 

 

Develop the linear regression equation for these data.   [4 POINTS]

 

How many units would a worker produce if they spent 18 minutes on the line?  [4 POINTS]

 

 Question 2.American Theaters knows that a certain hit movie ran an average (μ) of 84 days in each city, and the corresponding standard deviation (σ) was 10 days.  The manager of the southeastern district was interested in comparing the movie’s popularity in his region with that in all of American’s other theaters.  He randomly chose 75 theaters in his region and found that they ran the movie an average (x?) of 81.5 days.  At the 0.01 significance level, can the manager conclude that there was a significant difference in the length of the picture’s run between theaters in the southeastern district and all of American’s other theaters? 

 

Question 3.In Bigville, a fast-food chain feels it is gaining a bad reputation because it takes too long to serve the customers.  Because the chain has four restaurants in this town, it is concerned with whether all four restaurants have the same average service time.  One of the owners of the fast-food chain has decided to visit each of the stores and monitor the service time for five randomly selected customers.  At his four noontime visits, he records the following service times in minutes.  Do all the restaurants have the same mean service time?  (Use a = 0.05) 

 

 

 

Restaurant 1

 

3

 

4

 

5.5

 

3.5

 

4

 

Restaurant 2

 

3

 

3.5

 

4.5

 

4

 

5.5

 

Restaurant 3

 

2

 

3.5

 

5

 

6.5

 

6

 

Restaurant 4

 

3

 

4

 

5.5

 

2.5

 

3

 

 

 

Question 4. State Senator Hanna Rowe has ordered an investigation of the large number of boating accidents that have occurred in the state in recent summers.  Acting on her instructions, her aide, Geoff Spencer, has randomly selected 9 summer months within the last few years and has compiled data on the number of boating accidents that occurred during each of these months. The mean number of boating accidents to occur in these 9 months was 31 (x?), and the standard deviation (s) in this sample was 9 boating accidents per month.  Geoff was told to construct a 90% confidence interval for the true mean number of boating accidents per month.  What formula should Geoff use?

 

Question 5. Realtor Elaine Snyderman took a random sample of 12 homes in a prestigious suburb of Chicago and found the average appraised market value (x?) to be $780,000, and the standard deviation (s) was $49,000.  What formula would you use to test the hypothesis that for all homes in the area, the mean appraised value is less than $825,000?  (a = 0.05)

 

Question 6. R.V. Poppin, the concession stand manager for the local hockey rink, just had 2 cancellations on his crew.  This means that if more than 72,000 people come to tonight’s hockey game, the lines for hot dogs will constitute a disgrace to Mr. Poppin and will harm business at future games.  Mr. Poppin knows from experience that the number of people who come to the game is normally distributed with a mean (µ) of 67,000 and standard deviation (σ) of 4,000 people.  What formula should he use to determine the probability that there will be more than 72,000 people at the game?

 

Question 7. A law firm wants to determine the trend in its annual billings so that it can better forecast revenues.  It plots the data on its billings for the past 10 years and finds that the scatter plot appears to be linear.  What formula should they use to determine the trend line?

 

Question 8. Suppose that a random sample of 25 retail merchants from all of the 5,000 merchants in a large city yielded a mean advertising expense (x?) for the past year of $1,250.  If the annual advertising expenditures are known to be normally distributed and the standard deviation of the population (σ) is $750, what formula would you use to determine the 95% confidence interval for the true mean advertising expense?