A psychology class performed an experiment to determine whether a recall score in which instructions to form images of 25 words were given differs from an initial recall score for which no imagery instructions were given. Twenty students participated in the experiment with the results listed in the table:
| Student | With Imagery | Without Imagery | Student | With Imagery | Without Imagery |
| 1 | 20 | 5 | 11 | 17 | 8 |
| 2 | 24 | 9 | 12 | 20 | 16 |
| 3 | 20 | 5 | 13 | 20 | 10 |
| 4 | 18 | 9 | 14 | 16 | 12 |
| 5 | 22 | 6 | 15 | 24 | 7 |
| 6 | 19 | 11 | 16 | 22 | 9 |
| 7 | 20 | 8 | 17 | 25 | 21 |
| 8 | 19 | 11 | 18 | 21 | 14 |
| 9 | 17 | 7 | 19 | 19 | 12 |
| 10 | 21 | 9 | 20 | 23 | 13 |
(a) What two testing procedures can be used to test for differences in the distribution of recall scores with and without imagery? What assumptions are required for the parametric procedure? Do these data satisfy these assumptions?
(b) Use both the parametric and non-parametric tests for differences in the distributions of recall scores under these two conditions.
(c) Compare the results of the tests in part b. Are the conclusions for same? If not, why not?
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A psychology class performed an experiment to determine whether a recall score in which instructions to form images of 25 words were given differs from an initial recall score for which no imagery instructions were given. Twenty students participated in the experiment with the results listed in the table:
| Student | With Imagery | Without Imagery | Student | With Imagery | Without Imagery |
| 1 | 20 | 5 | 11 | 17 | 8 |
| 2 | 24 | 9 | 12 | 20 | 16 |
| 3 | 20 | 5 | 13 | 20 | 10 |
| 4 | 18 | 9 | 14 | 16 | 12 |
| 5 | 22 | 6 | 15 | 24 | 7 |
| 6 | 19 | 11 | 16 | 22 | 9 |
| 7 | 20 | 8 | 17 | 25 | 21 |
| 8 | 19 | 11 | 18 | 21 | 14 |
| 9 | 17 | 7 | 19 | 19 | 12 |
| 10 | 21 | 9 | 20 | 23 | 13 |
A study was conducted to compare the mean numbers of police emergency calls per 8-hour shift in two districts of a large city. Samples of 100 8-hour shifts were randomly selected from the police records for each of the two regions and the number of emergency calls was recorded for each shift. The sample statistics are listed here:
| Region | ||
| 1 | 2 | |
| Sample size | 100 | 100 |
| Sample mean | 2.4 | 3.1 |
| Sample variance | 1.4 | 2.64 |
A company plans to promote a new product by using one of three advertising campaigns. To investigate the extent of product recognition from these three campaigns, 15 market areas were selected and five were randomly assigned to each advertising plan. At the end of the ad campaigns, random samples of 400 adults were selected in each area and the proportions who were familiar with new product were recorded. The responses were not approximately normal. Is there a significant difference among the three population distributions from which these samples came? Use an appropriate nonparametric method to answer this question at 5% level of significance.
| Campaign | ||
| 1 | 2 | 3 |
| 0.33 0.29 0.21 0.32 0.25 | 0.28 0.41 0.34 0.39 0.27 | 0.21 0.30 0.26 0.33 0.31 |
If magnitude of earthquakes recorded in a region of a country follows a distribution with parameter µ whose pdf is given below:
f (x) = , -∞ < x, μ < ∞
then show that the estimators of the parameter µ using maximum likelihood and method of moments are same.
The following data relate to the number of items produced per shift by two workers for a number of days:
| Worker A | 19 | 22 | 24 | 27 | 24 | 18 | 20 | 19 | 25 | |
| Worker B | 26 | 37 | 40 | 35 | 30 | 40 | 26 | 30 | 35 | 45 |
A company plans to promote a new product by using one of three advertising campaigns. To investigate the extent of product recognition from these three campaigns, 15 market areas were selected and five were randomly assigned to each advertising plan. At the end of the ad campaigns, random samples of 400 adults were selected in each area and the proportions who were familiar with new product were recorded. The responses were not approximately normal. Is there a significant difference among the three population distributions from which these samples came? Use an appropriate nonparametric method to answer this question at 5% level of significance.
| Campaign | ||
| 1 | 2 | 3 |
| 0.33 0.29 0.21 0.32 0.25 | 0.28 0.41 0.34 0.39 0.27 | 0.21 0.30 0.26 0.33 0.31 |
A company plans to promote a new product by using one of three advertising campaigns. To investigate the extent of product recognition from these three campaigns, 15 market areas were selected and five were randomly assigned to each advertising plan. At the end of the ad campaigns, random samples of 400 adults were selected in each area and the proportions who were familiar with new product were recorded. The responses were not approximately normal. Is there a significant difference among the three population distributions from which these samples came? Use an appropriate nonparametric method to answer this question at 5% level of significance.