Q. 42 How are the variances of under randomsampling, proportional allocation and Neymanallocation related with each other?

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Answered: Q. 42 How are the variances of under…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2. The table below give the output for 6 years of an experimental farm that used each of 4 fertilizers. ASsume that the output with each fertilizer are normally distributed with equal variances. Test the hypothesis that the population means are the same at the .05 level of significance. Yield in Cavans Year Fertilizer 1 Fertilizer 2 Fertilizer 3 Fertilizer 2 1 49 46 55 50 58 2 57 51 61 3 56 58 52 57 4 52 61 60 65 47 50 48 61 6 59 48 57 53
Suppose a data set from a bike share company contains the number of daily bike rentals at each of 6 stations for the 23 weekdays of a particular month, i.e. we have Yij for i = 1, ..., 23 and j 1,...6. Write down a hierarchical normal model that can be used to estimate the mean number of bike rentals at each station. You can assume that the unknown variance o? of the number of bike rentals is the same for each station.
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A researcher wishes to select a stratified random sample from a population with 3 strata as follows (with the usual notation): Н Nh Sn Ch 1 300 30 25 500 40 49 3 200 20 36 If the budget is $5000 and the overheads $800, find the allocations for each stratum and estimate the variance of sample meanusing the allocation method. By using proportional allocation, estimate the variance and compare it to the variance from part (1). Determine the total cost from the allocation of part (2). Explain your result. (1) (2) (3)
Consider two inbred lines of guava trees, G1 and G2, grown on the same farm. The average diameter of G1 guavas is 6 cm, with a variance of 1.5 cm2, while the average diameter of G2 guavas is 8 cm. , with a variance of 2.8 cm2. Based on the description above, determine which of the following statements is false. MultipleChoice VE for G2 > 0 GV for G1 = 0 PV for G1 > PV for G2 VE for G1 >0
An employer asserts that it is justifiable to pay female employees more than male employees on the grounds that they are more productive. Suppose that the population hourly outputs of male and female employees are normally distributed but assumed to have non-constant variances. To determine if there is evidence to support the claim of the employer, data on hourly outputs of random samples of 15 female and 15 male employees were collected and shown below. Female 349 353 349 336 342 353 357 347 357 348 354 346 345 359 340 Male 304 343 344 313 340 319 348 338 339 351 345 369 360 326 340 a. Can the employer's assertion be substantiated at 5% level of significance? b. Perform another test this time at 1% level of significance and compare the result in (a). Explain.
a. A researcher carrying out an independent samples t-test, decides to use an unequal variance t-test (Welch's t-test). Why might they have decided to use this? options: The variance of group A in the study is 3.5 times greater than the variance of group B Box plots indicate that the distributions are strongly skewed The data for the two groups appear to be pseudo replicated The box plots indicate that there are outliers in the two distributions. b. A study which examines breast cancer survival rates at 5 different hospitals takes data from 30 patients at each hospital. This would be an example of a: Question 2 options: Simple random sampling design Stratified random sampling design Hierarchical sampling design Cluster sampling design
3. We want to compare initial salaries of graduates with Marketing major and graduates with Finance Major. We compare the salaries of these two groups with the same GPA. Example, salary of marketing graduate with GPA 3.5 is compare with the salary of Finance graduate with the same GPA 3.5. Assume salaries are normally distributed for both groups with unequal variances. We want to study the mean of the difference of these two groups. This is a a) t-test with equal variances b) t-test with unequal variances c) t-test for paired data.
A transect is an archaeological study area that is mile wide and 1 mile long. A site in a transect is the location of a significant archaeological find. Let x represent the number of sites per transect. In a section of Chaco Canyon, a large number of transects showed that x has a population variance . In a different section of Chaco Canyon, a random sample of 23 transects gave a sample variance for the number of sites per transect. Use an to test the claim that the variance in the new section is greater than 36.4. What is the level of significance? 90% 1% 5% 95% 10%
The following data are from a completely randomized design. In the following calculations, use a = 0.05. Treatment Treatment Treatment 2 3 64 82 69 47 71 53 54 87 60 35 64 46 50 76 57 2 148.67 108.67 96.67

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Q. 42 How are the variances of under random sampling, proportional allocation and Neyman allocation related with each other?