Question

(All in Excel) See the population data for Buena School District buses such as:
a) Determine the size of a sample of average bus maintenance, at a confidence level of 95% and with an estimated error of $ 25.
b) Construct the 95% confidence interval of the average maintenance of the buses.
c) Construct the confidence interval of 90% of the average mileage of the buses.

Maintenance
329
503
505
466
359
546
427
474
382
422
433
474
558
561
357
329
497
459
355
489
436
455
514
503
380
432
478
406
471
444
493
452
461
496
469
442
414
459
457
462
570
439
369
390
469
381
501
432
392
441
448
468
467
478
515
411
504
504
392
423
410
529
477
540
450
390
424
433
428
494
396
458
493
475
476
403
337
492
426
449

Answer 1

Step 1 : Find the mean and std. deviation for the maintenance variable.

00 D E F G H A 1 Maintenance 2 329 3 503 Mean 450.2875 =AVERAGE(A2:A81) Std. Deviation 53.34937 ESTDEV.P(A2:A81) N 80 =COUNT(A2:A81) 4 505 466 5 6 359 7 546 8 427 9 474 10 382 11 422 12 433 474 13 14 558 15 561 16 357 17 329 18 497 459 19 20 355 21 489 22 436 23 455 24 514 25 503 26 380 27 432

a) Determine the size of a sample of average bus maintenance, at a confidence level of 95% and with an estimated error of $ 25.

standard deviation = 0 = 53.34 margin of error = ME = 25 We need to find the sample size (n) Confidence interval = 0.95 alpha/2 = (1-0.95)/2= 0.025 We use normal distribution to find zstat Using the normal table, we find the zstat for alpha/2 = 0.025 zstat = 1.959964 We know ME= * zstat ME n= x zstat)? = ( 53,34 x 1.959964)? = 17.4873 Hence the sample size required is 17.4873

b) Construct the 95% confidence interval of the average maintenance of the buses.

We are given sample mean = ju= 450.2875 standard deviation = 53.3437 Confidence interval = 0.95 a/2 = (1-0.9572= 0.025 Using the Normal distribution table, we find the zstat for a/2 = 0.025 zstat = 1.96 Margin of error (ME) = zstat x se = 1.96 x 5.964007 11.6894537 Confidence Interval = pi + ME= 450.2875– 11.6894537 Therefore the 95% confidence interval for the mean is (438.598, 461.977) =

c. Data not give for the mileage variable