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) Estimate the difference in the true proportions favoring the bond proposal with a 99% confidence interval.
(b) If both samples were pooled into one sample of size n = 150, with 103 in favor of the proposal, provide a point estimate of the proportion of city residents who will vote for the bond proposal.
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 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 |
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.
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 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.