Descriptive Statistics and Test of Hypothesis

Helen managed a major manufacturing facility that was devoted largely to producing millions of identical small metallic parts. While the parts produced were (intended to be) identical, the facility produced them by using hundreds of presses, of three different types (which we'll call types 1, 2, and 3). The rated production rates for machine types 1, 2, and 3 were 700, 200, and 155 parts per minute, respectively, but actual production rates varied. Helen felt that factors such as quality of input material, worn or "changed-out" dies, and dirty or poorly maintained presses would probably affect production. Helen suspected that there could significant differences between the Rated Production Rates for each machine and the actual production rates. This could either be explained by differences in the supervisory effectiveness of the different managers or because there are significant differences in the downtown time for each of the three different machines

The facility had always kept daily production records, but from what Helen could tell, no one ever consulted them or did anything with them other than to put them in file cabinets at the end of each reporting period. She thought that in principle she should be able to monitor production rates for the types of machines, identify any machines that seemed to be in need of adjustment, and characterize the amount of downtime to be expected. Accordingly, she extracted one day's production records for 116 presses at her facility.

The machines were scheduled for a shift of 7.75 hours each day. The operators recorded the hours of operation manually on clipboards kept near each machine. The actual quantities of parts produced were determined from automatic counters on the machines. The data on MACHINE_PROD.SAV are derived from these logs.

Assignment:

1. Use the method of hypothesis testing to resolve the question of whether each machine is producing according to its rating. If a machine is producing at 85% or more of its rating, then that machine is within acceptable performance efficiency. Use the method of Hypothesis testing to determine which machine is within acceptable performance efficiency
2. Present your conclusions in a report. Please be sure to present tables or charts.

Data Definitions:(1)OBS= Machine ID Number (2)MTYPE= Type of Machine (3)PROD= Total Output of Machine during Hours of Operation (4)HRSWRK= Total Hours of Operation when Data was Taken (5)HRSDN= Total Down-Time during the Day

One-Sample Test Test Value = 595 99% Confidence Interval of the Difference Machine Type df Sig. (2-tailed) | Mean Difference Lower Upper Machine Type 1 Output per Minute 3.858 27 001 14.09326 12.4251 75.7614 Test Value 99% Confidence Interval of the Difference Machine Type df Sig. (2-tailed) |Mean Difference Lower Upper Machine Type 3 Output per Minute 3.629 52 001 24.48084 6.4432 42.5184 Test Value = 170 99% Confidence Interval of the Difference Machine Type df Sig. (2-tailed) Mean Difference Lower Upper Machine Type 2 Output per Minute -21.215 34 000 -49.23545 -55.5675 42.9034 One-Sample Statistics Machine Type N Mean Std. Deviation Std. Error Mean Machine Type 1 Output per Minute 28 539.093 60.48050 11.42974 One-Sample Statistics Machine Type N Mean Std. Deviation Std. Error Mean Machine Type 3 Output per Minute 53 156.4808 19.11321 6.74622 One-Sample Statistics Machine Type N Mean Std. Deviation Std. Error Mean Machine Type 2 Output per Minute 35 120.7646 13.73011 2.32081