Question

A scientist wants to check the yield of wheat from different varieties of wheat. In this regards, the yields of wheat from 16 plots, all of approximately equal fertility, when 4 varieties of wheat (Say, A, B, C and D) were cultivated are recorded in the following table:

Plot No. 1 2 3 4 5 6 7 8
Variety: A B D C B C A D
Yield: 42 44 39 41 43 44 44 36
Plot No.: 9 10 11 12 13 14 15 16
Variety: B D A C B A B C
Yield: 46 40 43 45 47 45 45

42

Assuming that the yields of wheat are normally distributed in each variety with approximately equal variances, test the hypothesis that the average yields of wheat in all four varieties of wheat are the same at 1% level of significance.  

06 Feb 2021
Answer :
Word Count : 831

To test the hypothesis that the average yields of wheat in all four varieties are the same, we will perform an analysis of variance (ANOVA). This test helps to determine whether there are significant differences in the means of the yields among the four wheat varieties.

Step 1: State the Hypotheses

The null hypothesis (H₀) is that the average yield of wheat is the same for all four varieties. The alternative hypothesis (H₁) is that at least one of the varieties has a different average yield.

  • Null Hypothesis (H₀): μ₁ = μ₂ = μ₃ = μ₄ (the mean yields of all four varieties are equal)
  • Alternative Hypothesis (H₁): At least one of the mean yields is different

Step 2: Organize the Data

We are given the following data of yields for the four varieties:

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Related Questions

Twenty operators are working in a particular department of a call centre. The longserving operators feel that they should have a promotion based on length of service built into their job structure. For assessment of their efficiency, the personnel department produces a score of efficiency based on various parameters. The efficiency scores along with their length of service are given below:

S. No. Length of Service Efficiency Scores
1 2 72
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Suppose that a customer service manager of a mall wants to evaluate the service of the eight food counters in the mall. She/he hires seven evaluators with varied experience in food-service evaluation to act as raters. To reduce the effect of the variability from rater to rater, a randomised block design is applied considering raters serving as the blocks. The seven raters evaluate the service of each of the eight food counters in a randomorder. A rating scale from 0 (low) to 100 (high) is used. The following table summarises the results:

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1 70 61 82 74 68 59 80 81
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The effect of evaluation of each rater on the service of food counters is normally distributed with approximately equal variances.

i) Analyse the design at 2% level of significance.

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1 204 462 51 521 239
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4 364 284 54 490 175
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6 368 304 56 310 384
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14 491 230 64 270 495
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16 311 322 66 484 440
17 434 349 67 173 418
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21 289 352 71 323 409
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26 485 239 76 423 461
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31 324 365 81 205 274
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49 161 495 99 426 381
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Answer the following:

i) Which mobile brand has more average sales?

ii) Which mobile brand shows greater variability in the sales?

iii) Compute the skewness and kurtosis for the given data and interpret the results.

iv) Determine the correlation between both mobiles.

v) Compute suitable width of the class intervals for both brands,

vi) Construct the continuous frequency distribution for both brands.

vii)Represent the raw data as well as grouped data using suitable diagram/graph.  

A scientist wants to check the yield of wheat from different varieties of wheat. In this regards, the yields of wheat from 16 plots, all of approximately equal fertility, when 4 varieties of wheat (Say, A, B, C and D) were cultivated are recorded in the following table:

Plot No. 1 2 3 4 5 6 7 8
Variety: A B D C B C A D
Yield: 42 44 39 41 43 44 44 36
Plot No.: 9 10 11 12 13 14 15 16
Variety: B D A C B A B C
Yield: 46 40 43 45 47 45 45

42

Assuming that the yields of wheat are normally distributed in each variety with approximately equal variances, test the hypothesis that the average yields of wheat in all four varieties of wheat are the same at 1% level of significance.  

ii) Are the variances of the distributions of mobiles of Brand A and Brand B equal at 5 % level of significance?

i) Is there enough evidence that the average sales of mobile of Brand A is more than the average sales of the Brand B at 5 % level of significance?

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