Question

A manufacturing company produces steel housings for electrical equipment. The main component part of the housing is a steel trough that is made out of a 14-gauge steel coil. It is produced using a 250-ton progressive punch press with a wipe-down operation that puts two 90-degree forms in the flat steel to make the trough. The distance from one side of the form to the other is critical because of weatherproofing in outdoor applications. The company requires that the width of the trough be between 8.31 inches and 8.61 inches. The data below represents the widths of the troughs, in inches, for a sample of n = 49: 8.312 8.343 8.317 8.383 8.348 8.410 8.351 8.373 8.481 8.422 8.476 8.382 8.484 8.403 8.414 8.419 8.385 8.465 8.498 8.447 8.436 8.413 8.489 8.414 8.481 8.415 8.479 8.429 8.458 8.462 8.460 8.444 8.429 8.460 8.412 8.420 8.410 8.405 8.323 8.420 8.396 8.447 8.405 8.439 8.411 8.427 8.420 8.498 8.409

(a) At the 0.05 level of significance, is there evidence that the mean width of the troughs is different from 8.46 inches? Be sure to include the following in your answer:

i. List the null and alternate hypotheses

ii. Find the value of the test statistic iii. List the decision rule.

iv. Conclude in a complete sentence and include why you decided as you did – referring to the decision rule.

(b) What assumption about the population distribution is needed in order to conduct the t test in (a)?

Answer 1

(a)(i) Null hypothesis: H: 4 = 8.46 The mean width of the troughs is 8.46 inches. Alternative hypothesis: H: 1+8.46 The mean width of the troughs is different from 8.46 inches. (ii) MINITAB output:

One-Sample T: Sample Test of u = 8.46 v3 # 8.46 Variable Sample N 49 Mean 8.42090 St Dev 0.04611 SE Mean 0.00659 95% CI (8.40765, 8.43414) TP -5.94 0.000 The value of the test statistic is t= -5.94. 111 Decision rule: If p-values a(=0.05), then reject the null hypothesis H. (iv) Conclusion: Since p-value =0) sa (= 0.05), then reject the null hypothesis H. There is sufficient evidence that the mean width of the troughs is different from 8.46 inches.

(b) The population from which samples are drawn is normally distributed.