The first item on Ted Thorndike’s agenda for today is a meeting with Martha Scott, a technical sales representative with Cromwell Industries. Cromwell produces a racquet- stringing machine that is promoted as being the fastest in the industry. In their recent telephone conversation, Martha offered Ted the chance to try the machine for a full week, then return it to Cromwell if he decides it doesn’t offer a worthwhile improvement. Currently, the Thorndike racquetball and tennis racquets are strung using a type of ma- chine that has been around for about 10 years, and the Thorndikes have been very pleased with the results. When efficiency experts visited the plant last year, they found it took an average of 3.25 minutes to string a racquetball racquet and an average of 4.13 minutes for a tennis racquet. Both distributions were found to be approximately normal. Ms. Scott comes by, explains the operation of the machine, and assists in its installation. Because its controls are similar in function and layout to the older model, no operator training is necessary. During the 1-week trial, the new machine will be working side-by- side with older models in the racquet-stringing department. After Ms. Scott leaves, Luke and Ted Thorndike discuss the machine further. Luke indicates that the oldest of the current machines is about due for replacement and, if the Cromwell model is really faster, he will buy the Cromwell to replace it. It’s possible that Cromwell models would also be purchased as other stringing machines approach the end of their operating lifetimes and are retired. Luke cautions Ted that the Cromwell must be purchased only if it is indeed faster than the current models. The Cromwell must be quicker in stringing both racquetball racquets and tennis racquets. Otherwise, the firm will continue purchasing and using the current model. Evaluating the Cromwell model, Ted measures the exact time required for each racquet in separate samples consisting of 40 racquetball racquets and 40 tennis racquets. The times are given in data file CROMWELL. Since Luke seems quite adamant against buying something that isn’t any faster than the current models, Ted must be very confident (let’s say 99% certain) that any increased speeds measured are not simply due to chance. (a) At the 0.01 level of significance, do the respective tests appear to warrant purchase of the Cromwell machine, or should it be returned to Cromwell at the end of the week? It can be solved using excell. here is the data: RBRacq TennRacq 2.97 3.77 3.11 3.51 2.97 3.91 2.70 4.49 3.14 3.71 3.43 3.97 3.26 3.43 3.09 4.47 3.17 3.74 3.36 3.77 3.10 4.08 3.36 4.31 3.18 4.27 3.16 4.17 3.89 3.90 2.79 4.36 3.48 3.84 2.71 3.70 3.16 3.68 3.21 4.14 3.41 3.85 3.09 3.86 3.41 3.80 3.24 4.09 3.13 4.03 3.22 4.65 3.06 3.50 2.83 4.54 2.91 4.27 2.92 4.61 3.36 3.89 2.67 4.23 3.20 4.46 3.34 3.84 2.94 3.63 3.46 3.99 3.13 3.88 3.32 3.97 2.97 3.51 3.18 4.62
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
The first item on Ted Thorndike’s agenda for today is a meeting with Martha Scott, a technical sales representative with Cromwell Industries. Cromwell produces a racquet- stringing machine that is promoted as being the fastest in the industry. In their recent telephone conversation, Martha offered Ted the chance to try the machine for a full week, then return it to Cromwell if he decides it doesn’t offer a worthwhile improvement.
Currently, the Thorndike racquetball and tennis racquets are strung using a type of ma- chine that has been around for about 10 years, and the Thorndikes have been very pleased with the results. When efficiency experts visited the plant last year, they found it took an average of 3.25 minutes to string a racquetball racquet and an average of 4.13 minutes for a tennis racquet. Both distributions were found to be approximately normal.
Ms. Scott comes by, explains the operation of the machine, and assists in its installation. Because its controls are similar in
After Ms. Scott leaves, Luke and Ted Thorndike discuss the machine further. Luke indicates that the oldest of the current machines is about due for replacement and, if the Cromwell model is really faster, he will buy the Cromwell to replace it. It’s possible that Cromwell models would also be purchased as other stringing machines approach the end of their operating lifetimes and are retired. Luke cautions Ted that the Cromwell must be purchased only if it is indeed faster than the current models. The Cromwell must be quicker in stringing both racquetball racquets and tennis racquets. Otherwise, the firm will continue purchasing and using the current model.
Evaluating the Cromwell model, Ted measures the exact time required for each racquet in separate samples consisting of 40 racquetball racquets and 40 tennis racquets. The times are given in data file CROMWELL.
Since Luke seems quite adamant against buying something that isn’t any faster than the current models, Ted must be very confident (let’s say 99% certain) that any increased speeds measured are not simply due to chance.
(a) At the 0.01 level of significance, do the respective tests appear to warrant purchase of the Cromwell machine, or should it be returned to Cromwell at the end of the week?
It can be solved using excell. here is the data:
| RBRacq | TennRacq |
| 2.97 | 3.77 |
| 3.11 | 3.51 |
| 2.97 | 3.91 |
| 2.70 | 4.49 |
| 3.14 | 3.71 |
| 3.43 | 3.97 |
| 3.26 | 3.43 |
| 3.09 | 4.47 |
| 3.17 | 3.74 |
| 3.36 | 3.77 |
| 3.10 | 4.08 |
| 3.36 | 4.31 |
| 3.18 | 4.27 |
| 3.16 | 4.17 |
| 3.89 | 3.90 |
| 2.79 | 4.36 |
| 3.48 | 3.84 |
| 2.71 | 3.70 |
| 3.16 | 3.68 |
| 3.21 | 4.14 |
| 3.41 | 3.85 |
| 3.09 | 3.86 |
| 3.41 | 3.80 |
| 3.24 | 4.09 |
| 3.13 | 4.03 |
| 3.22 | 4.65 |
| 3.06 | 3.50 |
| 2.83 | 4.54 |
| 2.91 | 4.27 |
| 2.92 | 4.61 |
| 3.36 | 3.89 |
| 2.67 | 4.23 |
| 3.20 | 4.46 |
| 3.34 | 3.84 |
| 2.94 | 3.63 |
| 3.46 | 3.99 |
| 3.13 | 3.88 |
| 3.32 | 3.97 |
| 2.97 | 3.51 |
| 3.18 | 4.62 |
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