For all problems requiring inference, you can use a = 0.05 or 1 – a = 0.95 unless otherwise stated.
A math instructor is comparing two methods of teaching, a modern method and a traditional method. She uses the modern method for one class (of size 25 students) and the traditional method for another class (of size 25 students, who are different people from the first class). The two sets of students can be considered samples from the two populations of students that would take this class taught with the two methods. The question of interest is to compare the population mean final exam scores for the two methods. The instructor does not know ahead of time which method is likely to produce better results. The data and some SAS code are given on the course website. Note from the output that the sample mean of the “modern method” scores is 77.776, with a sample standard deviation of 9.298. Also, the sample mean of the “traditional method” scores is 81.972, with a sample standard deviation of 1.976. Write a mini-report describing a data analysis of your choice and your conclusions to answer the instructor’s research question.
| Moments | |||
| N | 25 | Sum Weights | 25 |
| Mean | 77.776 | Sum Observations | 1944.4 |
| Std Deviation | 9.29808582 | Variance | 86.4544 |
| Skewness | -0.0859061 | Kurtosis | -0.4485726 |
| Uncorrected SS | 153302.56 | Corrected SS | 2074.9056 |
| Coeff Variation | 11.954955 | Std Error Mean | 1.85961716 |
| Basic Statistical Measures | |||
| Location | Variability | ||
| Mean | 77.77600 | Std Deviation | 9.29809 |
| Median | 78.60000 | Variance | 86.45440 |
| Mode | 79.80000 | Range | 34.70000 |
| Interquartile Range | 11.40000 | ||
| Tests for Location: Mu0=0 | ||||
| Test | Statistic | p Value | ||
| Student’s t | t | 41.82366 | Pr > |t| | <.0001 |
| Sign | M | 12.5 | Pr >= |M| | <.0001 |
| Signed Rank | S | 162.5 | Pr >= |S| | <.0001 |
| Quantiles (Definition 5) | |
| Level | Quantile |
| 100% Max | 93.5 |
| 99% | 93.5 |
| 95% | 92.3 |
| 90% | 92.2 |
| 75% Q3 | 83.1 |
| 50% Median | 78.6 |
| 25% Q1 | 71.7 |
| 10% | 63.4 |
| 5% | 63.3 |
| 1% | 58.8 |
| 0% Min | 58.8 |
| Extreme Observations | |||
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| 58.8 | 16 | 88.1 | 13 |
| 63.3 | 17 | 89.7 | 18 |
| 63.4 | 23 | 92.2 | 5 |
| 69.4 | 11 | 92.3 | 19 |
| 70.0 | 3 | 93.5 | 22 |
| Moments | |||
| N | 25 | Sum Weights | 25 |
| Mean | 81.972 | Sum Observations | 2049.3 |
| Std Deviation | 1.9757952 | Variance | 3.90376667 |
| Skewness | 0.56995457 | Kurtosis | -0.2894089 |
| Uncorrected SS | 168078.91 | Corrected SS | 93.6904 |
| Coeff Variation | 2.41032938 | Std Error Mean | 0.39515904 |
| Basic Statistical Measures | |||
| Location | Variability | ||
| Mean | 81.97200 | Std Deviation | 1.97580 |
| Median | 81.50000 | Variance | 3.90377 |
| Mode | 80.30000 | Range | 7.60000 |
| Interquartile Range | 2.90000 | ||
| Note: The mode displayed is the smallest of 2 modes with a count of 3. |
| Tests for Location: Mu0=0 | ||||
| Test | Statistic | p Value | ||
| Student’s t | t | 207.4405 | Pr > |t| | <.0001 |
| Sign | M | 12.5 | Pr >= |M| | <.0001 |
| Signed Rank | S | 162.5 | Pr >= |S| | <.0001 |
| Quantiles (Definition 5) | |
| Level | Quantile |
| 100% Max | 86.0 |
| 99% | 86.0 |
| 95% | 85.9 |
| 90% | 85.3 |
| 75% Q3 | 83.4 |
| 50% Median | 81.5 |
| 25% Q1 | 80.5 |
| 10% | 80.3 |
| 5% | 79.7 |
| 1% | 78.4 |
| 0% Min | 78.4 |
| Extreme Observations | |||
| Lowest | Highest | ||
| Value | Obs | Value | Obs |
| 78.4 | 40 | 83.5 | 33 |
| 79.7 | 30 | 84.0 | 28 |
| 80.3 | 49 | 85.3 | 26 |
| 80.3 | 45 | 85.9 | 42 |
| 80.3 | 41 | 86.0 | 46 |
