Question

Question 5) Does standard deviation weight differ from 2 grams if the standard deviation of the sample is 2.067 grams (α=0.05)?

48 students participated in evaluating small package of skittles. The following table shows the result of this study. Assume the weight of skittles are normally distributed with standard deviation of 2 grams. Net Weight Green Red Yellow Brown Orange Count 2923 Total 2978.4 576 589 641 531 586 Sample Mean 62.05

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Answer 1

Given that, s = 2.067, n= 48 Null hypothesis: H:0 = 2 Alternative hypothesis: H:0 #2 Level of significance, a = 0.05 Test statistic: m? (n-1). (48-1)2.0672 = 50.2017 50.20 Degree of freedom: n - 1 = 48-1 = 47 Critical value: x1 = 29.956, v = 67.821 Decision rule: Reject H,, if x > Xi orx <x otherwise do not reject H,. Since the test statistic (50.20) is less than the critical value (67.821), so we fail to reject the null hypothesis at 5% significance level. Conclusion: There is no sufficient evidence to support the claim that standard deviation weight differ from 2 grams Active