Define Volcano. Discuss the different types of volcanoes with the help of neat sketches.
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Explain Airy's and Pratt's views on isostasy with the help of suitable figures.
See Answer →Define fog. Discuss the different types of fog with the help of neat sketches.
See Answer →In order to compare the mileage yields of 3 kinds of Gasoline, several tests were run, and the following results were obtained:
Gasoline A: 19 21 20 18 21 21
Gasoline B: 23 20 22 20 24 23
Gasoline C: 20 17 21 19 20 17
See Answer →Household Distribution by Village
| Village | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| No. of Households | 35 | 28 | 20 | 25 | 30 | 19 | 10 | 12 | 18 | 15 |
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A population consists of 10 villages with a total of 212 households. The second column of the accompanying table shows the number of households corresponding to each village. Select a PPS with replacement sample of 6 villages by using the Cumulative Total method:
I've transcribed the data from the image into a clean Markdown table for you.
See Answer →A sample of 60 students is to be drawn from a population consisting of 600 students belonging to two villages, A and B. The means and standard deviations of their marks are give below:
Based on the image provided, here is the data organized into a clear table:
| Villages | Stratum sizes ($N_i$) | Means ($x_i$) | Standard deviations |
|---|---|---|---|
| Village A | 400 | 60 | 20 |
| Village B | 200 | 120 | 80 |
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Draw all possible samples of size 2 from the population [2, 3, 4] and verify that E(X) = X Also find variance of X.
See Answer →State whether the following statements are true or false and also give the reason in support of your answer:
a) The total number of all possible samples of size 2 without replacement from a population of size 7 is 49.
b) RBD is suitable in situations where it is not possible to divide the experimental material into a number of homogeneous blocks.
c) If experimental error is reduced considerably and the efficiency of the design is decreased.
d) If strata are heterogeneous then stratified sampling schemes provides estimates with greater precision.
e) As we increase the sample size, representativeness of the population by the sample decreases.
See Answer →Two independent groups of patients were given Drug X and Drug Y. The recovery times (in days) are as follows:
| Drug X | 8 | 10 | 9 | 7 | 11 |
| Drug Y | 6 | 7 | 5 | 8 | 6 |
(i) State the null and alternative hypotheses.
(ii) Explain why the Mann–Whitney U test is appropriate for this data.
(iii) Perform the test at the 5% level of significance and draw a conclusion.
See Answer →Suppose the number of breakdowns per month in a factory follows a Poisson distribution with parameter λ.
(i) Find the Cramer-Rao lower bound for an unbiased estimator of λ.
(ii) Obtain the UMVUE of λ.
(i) Find the Cramer-Rao lower bound for the variance. (ii) Also, find the UMVUE of $\lambda$.
See Answer →A pharmaceutical company fills medicine bottles with a target weight of 500 mg. It is known that the filling weights are normally distributed with known variance o² = 16. Derive the likelihood ratio test for testing
Ηο: μ = 500againstH₁: μ ≠ 500
at significance level a.
See Answer →State whether the following statements are True or False. Give reasons in support of your answer:
(i) When the population distribution is unknown and the data are measured on a nominal scale, the Sign test can be used to test a hypothesis about the median.
(ii) In the Bayesian framework, prior information about the parameter is combined with the likelihood to obtain the posterior distribution.
(iii) The Wilcoxon rank-sum test is a non-parametric alternative to the two-sample t-test when normality is not assumed.
(iv) A complete sufficient statistic guarantees the uniqueness of the unbiased estimator obtained through it.
(v) The power of a statistical test is the probability of accepting the null hypothesis when it is true.
See Answer →What is a research report? Explain the types of research reports and discuss the principles of effective report writing.
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Discuss research ethics. Explain issues related to plagiarism, informed consent, confidentiality, and ethical responsibility of researchers.
See Answer →Discuss the methods of data collection. Explain primary and secondary data, their sources, advantages, and limitations.
See Answer →What is a hypothesis? Explain the types of hypotheses. Describe the procedure for hypothesis testing in detail.
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