In exercises that call for two-sample procedures, you may use either of the two approximations for the degrees of freedom that we have discussed: the value given by your software or the smaller of and . Be sure to state clearly which approximation you have used.

Question 7.55

7.55 Counts of seeds in one-pound scoops.

Refer to Exercise 7.23 (pages 375–376). As part of the Six Sigma quality improvement effort, the company wants to compare scoops of seeds from two different packaging plants. An SRS of 50 one-pound scoops of seeds was collected from Plant 1746, and an SRS of 19 one-pound scoops of seeds was collected from Plant 1748. The number of seeds in each scoop were recorded.

seedcnt2

  1. Using this data set, create a histogram, boxplot, and Normal quantile plot of the seed counts from Plant 1746. Do the same for Plant 1748. Are the distributions reasonably Normal? Summarize the distributions in words.
  2. Are the procedures appropriate given your observations in part (a)? Explain your answer.
  3. Compare the mean number of seeds per one-pound scoop for these two manufacturing plants using a 99% confidence interval.
  4. Test the equality of the means using a two-sided alternative and a significance level of 1%. Make sure to specify the test statistic, degrees of freedom, and -value.
  5. Write a brief summary of your procedures assuming your audience is the company CEO and the two plant managers.

7.55

(a) For plant 1746: the data are roughly Normal. For plant 1748: the data are somewhat left-skewed but have several clusters or groups of points. (b) Because the total , the procedures are appropriate. (c) For 1746: . For 1748: . Using , the 99% C.I. is (−418.4, −76.8). (d) . The data are significant at the 1% level, and there is evidence that the mean number of seeds per 1-pound scoop is different for the two plants. (e) Answers will vary. The emphasis should be on the difference between the number of seeds so that potentially the scoops from plant 1746 are too light or the scoops from plant 1748 are too heavy (assuming the seeds are the same size/weight).