A snowmobile company makes an average of 9 engines

A snowmobile company makes an average of 9 engines/day, with engine average output of 10 horsepower (hp) based on historical record. No other information is available. Please show formulae used in each answer.

 

1. During the day of Monday, 9 engines were made and tested at with average = 11 hp and sample standard deviation = 5.0. Did the factory experience a problem in materials or methods for the day that was significant?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer significant difference (Monday sample average versus historical record): Yes________, No_________

 

2. What is the maximum acceptable average engine horsepower that can be produced based on Monday production data (9 engines were made and tested with average = 11 hp and standard deviation = 5.0)?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer maximum acceptable average engine horsepower on Monday______________

 

3. A check of the company records indicated that over the last week, 30 engines were made, with and average or 10 hp and standard deviation of 3. Given this new information, does the answer in question 1 change?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer significant difference (Monday sample average versus historical record): Yes________, No_________

 

4. For the situation described in problem 3, (a check of the company records indicated that over the last week, 30 engines were made, with average = 10 and standard deviation of 3). What is the maximum acceptable average engine horsepower that can be produced in this factory for a typical day production of 9 units?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Max Acceptable average horse power for a typical Day  ________

 

5. Is the variability of the 9 engines made on Monday (with average = 11 hp and standard deviation = 5.0) significantly different from last week’s engine Standard deviation (=3) of 30 engines?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer Significant Variability difference Monday versus last week Yes________, No___________

 

6. Management decided to check the engines made on Tuesday. Seven (7) engines were made with average = 9 hp and standard deviation = 2.0. Ignoring the historical record and the data from the previous week, is the 7 engines average output = 9 on Tuesday significantly different than the 9 engines on Monday (11 average and sigma = 5.0)? Please extrapolate from the t table for the answer

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer Significant Average difference Monday versus Tuesday (w/o historical record) Yes______, No_____

 

7. Can the management test for the assumption that the engine variances (9 engines on Monday with 11 average and sigma = 5.0 and 7 engines on Tuesday average 9 hp and standard deviation = 2.0 are significant based on the Monday and Tuesday variance outputs?

Test Type: Z______, t______, d________, Chi SQ_______, F ______, Confidence interval_____,

Answer Significant Variance difference Monday versus Tuesday Yes________, No___________

 

8. Historically the engines yields a Mean µ = 10 hp and s = 3.0. A new engine is being developed. How many engines are needed to test to insure (95% confidence) that new mean is within .5 hpof the old engine?

Formulas:n =______________; Please show Calculations: