Question

Because of the rising costs of industrial accidents, many chemical, mining, and manufacturing firms have instituted safety courses. Employees are encouraged to take these courses designed to heighten safety awareness among them. A company is trying to decide which one of two courses to institute. To help make a decision, eight employees take course 1, and another group of eight take course 2. Each employee takes a test, which is graded out of a possible 25 marks. The safety test results of these employees are shown below. Assume that the scores are normally distributed. Course 1 Course 2 12.3750 19.1250 Sample Mean Sample Standard Deviation 2.7222 2.9970 Do these data provide enough evidence at the 5% level of significance to infer that the marks from course 1 are lower than those of course 2?

Answer 1

- The given data is, course course 2 12.3750 19.1250 Sample mean Sample Standard Dersation Sample size 2. 7222 2.9970 orod x =5.). The Hypothesis Ho: Mi= 42 VS HA ll < 42 The test statistic is . teau - Gita) A tcal = 12.3750 - 19. 1250 (2.7202)2 (2-9970)2 + (2.99 8

tcal = -6.75 0.9268 +1:1208 = -6.75 2-049.05 - 6.75 1.4815 - 4.7153 Heol, p. value = pr tal < -4.7153] = p [ tras 7 4.7153] 0.000166 - df = 0402-2 = 8+8-2 d = 14 I p. volue = 0.0002 so, So, yes, against p. volue = 0.0002 < 0:0.05 we Reet Ho at 51 level of significance. The given dato pooride us endence the null hapothesis Ho,