tate whether the following statements are True or False. Give reason in support of your answer:
(a) If the probability of non rejection of Ho when H, is true is 0.4 then power of the test will be 0.6.
(b) If T₁ and T₂ are two estimators of the parameter & such that Var(T1)-1/n and Var(T2)n then T, is more efficient than T2.
(c) A 95% confidence interval is smaller than 99% confidence interval.
(d) If the level of significance is the same, the area of the rejection region in a two-tailed test is less than that in a one-tailed test.
(e) Non parametric tests are more powerful than the parametric tests.
(a) True. The power of a test is given by \( 1 - \beta \), where \( \beta \) is the probability of failing to reject \( H_0 \) when \( H_1 \) is true. Given that _____ ______ _____ _______ __________ ____ ___ ____.
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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 | 12 |
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 |
If magnitude of earthquakes recorded in a region of a country follows a distribution with parameter a whose pdf is given below:
then show that the estimators of the parameter u using maximum likelihood and method of moments are same.
If a finite population has four elements: 6, 1, 3, 2.
(a) How many different samples of size n=2 can be selected from this population if you sample without replacement?
(b) List all possible samples of size n=2.
(c) Compute the sample mean for each of the samples given in part b.
(d) Find the sampling distribution off and draw the histogram.
(e) Compute standard error.
(f) If all four population values are equally likely, calculate the value of the population mean ? Do any of the samples listed in part (b) produce a value off exactly equal to
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-50 residents in the developing section and n100 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 Proposal
| Developing Section | Rest of the City | |
| Sample size | 50 | 100 |
| Number favoring proposa | 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. then show that the estimators of the parameter u using maximum likelihood and method of moments are same.
| Campaign | ||
| 1 | 2 | 3 |
| 0.33 | 0.28 | 0.21 |
| 0.29 | 0.41 | 0.30 |
| 0.21 | 0.34 | 0.26 |
| 0.32 | 0.39 | 0.33 |
| 0.25 | 0.27 | 0.31 |
tate whether the following statements are True or False. Give reason in support of your answer:
(a) If the probability of non rejection of Ho when H, is true is 0.4 then power of the test will be 0.6.
(b) If T₁ and T₂ are two estimators of the parameter & such that Var(T1)-1/n and Var(T2)n then T, is more efficient than T2.
(c) A 95% confidence interval is smaller than 99% confidence interval.
(d) If the level of significance is the same, the area of the rejection region in a two-tailed test is less than that in a one-tailed test.
(e) Non parametric tests are more powerful than the parametric tests.