Question

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?

06 Feb 2021
Answer :
Word Count : 703

To test if there is enough evidence to suggest that the average sales of Brand A are more than the average sales of Brand B at the 5% level of significance, we can conduct a hypothesis test. Since we are comparing the means of two independent groups (Brand A and Brand B), we can use a two-sample t-test.

### Step 1: Define the Hypotheses

- Null Hypothesis (H₀): The average sales of Brand A are equal to or less than the average sales of Brand B. Mathematically, we can express this as:
  \[
  H_0: \mu_A \leq \mu_B
  \]
  
- Alternative Hypothesis (H₁): The average sales of Brand A are greater than the average sales of Brand B. Mathematically, we express this as:
  \[
  H_1: \mu_A > \mu_B
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Related Questions

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

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
2 9 90
3 5 74
4 9 88
5 4 70
6 5 77
7 6 77
8 5 78
9 7 87
10 6 80
11 4 72
12 8 83
13 8 84
14 7 84
15 8 85
16 7 90
17 3 69
18 5 89
19 7 90
20 5 79

 Compute the Spearman’s rank correlation coefficient between the length of service and efficiency scores? Also compare this coefficient with Pearson’s correlation coefficient

A mobile manufacturing company distributed a newly launched mobile to 100 retail stores. These stores also sell another famous brand of mobile having same features. The manager of the company wants to compare the popularity of the newly launched mobile (say, Brand A) with the other popular mobile (say, Brand B). For this purpose, she selects a sample of 100 stores and noted the total number of sold mobiles of each brand. The data are recorded in the following table:

Store No. Brand A Brand B Store No. Brand A Brand B
1 204 462 51 521 239
2 328 454 52 327 284
3 262 211 53 531 225
4 364 284 54 490 175
5 478 168 55 427 365
6 368 304 56 310 384
7 506 162 57 433 182
8 362 328 58 313 505
9 151 484 59 424 270
10 371 256 60 295 183
11 522 159 61 288 463
12 328 362 62 239 517
13 532 178 63 244 435
14 491 230 64 270 495
15 428 392 65 224 449
16 311 322 66 484 440
17 434 349 67 173 418
18 314 339 68 256 498
19 425 312 69 416 410
20 296 446 70 233 546
21 289 352 71 323 409
22 240 467 72 279 529
23 245 392 73 340 214
24 271 293 74 464 262
25 225 500 75 383 216
26 485 239 76 423 461
27 174 283 77 351 497
28 257 380 78 404 271
29 417 295 79 226 475
30 234 466 80 164 511
31 324 365 81 205 274
32 280 449 82 329 295
33 341 189 83 263 326
34 465 218 84 365 157
35 384 530 85 479 368
36 424 321 86 369 256
37 352 485 87 507 272
38 405 369 88 363 226
39 227 457 89 163 334
40 165 420 90 372 218
41 203 293 91 523 184
42 327 315 92 329 437
43 261 399 93 533 206
44 363 409 94 492 177
45 477 213 95 429 173
46 367 256 96 177 502
47 505 190 97 435 406
48 361 238 98 315 358
49 161 495 99 426 381
50 370 428 100 297 408

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.  

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?

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:

  Food Counters
Raters A B C D E F G H
1 70 61 82 74 68 59 80 81
2 77 75 88 76 75 73 86 87
3 76 67 90 80 74 65 82 88
4 80 63 87 76 78 61 85 86
5 84 66 92 84 82 64 90 91
6 78 68 94 86 76 66 80 92
7 77 75 88 76 75 73 86 84

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.

ii) Is the average service of the eight food counters significantly different? If the difference between the averages services of the eight restaurants is significant, do the pair-wise comparison between them 

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