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 |
Can it be inferred that Worker A is more stable worker compared to B by testing the variation in the item produced by them at 5% level of significance .
Here, we want to test that worker A is more stable than worker B. As we know that stability of data is related to variance of the data. Smaller
value of the variance implies data that it is more stable. Therefore, to compare stability of two workers, it is enough to compare their variances. If σ12 and σ22 denote the variances of worker A and worker B respectively then our claim is
σ12 > σ22 and its complement is σ12 =< σ22. Since complement contains the
equality sign so we can take the complement as the null hypothesis and ________ _______ ____ __________ _________ __________ __________ _____ ________ ___ ___ ________.
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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 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 bond proposal for school construction will be submitted to the voters at the next municipal election. A major portion of the money derived form this bond issue will be used to build schools in a rapidly developing selection of the city, and the remainder will be used to renovate and update school buildings in the rest of the city. To assess the viability of the bond proposal, a random sample of 1 n 50 = residents in the developing section and 2 n 100 = residents from the other parts of the city were asked whether they plan to vote for the proposal. The results are tabulated below
Sample Values for Opinion on Bond Proposa
| Developing Section | Rest of the City | |
| Sample size | 50 | 100 |
| Number favoring proposal | 38 | 65 |
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.
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 |