1 answer

Long-distance runners have contended that moderate exposure to ozone increases lung capacity. To investigate this possibility,...

Question:

Long-distance runners have contended that moderate exposure to ozone increases lung capacity. To investigate this possibility, a researcher exposed 12 rats to ozone at the rate of 2 parts per million for a period of 30 days. The lung capacity of the rats was determined at the beginning of the study and again after the 30 days of ozone exposure. The lung capacities (in mL) are given here.

Before Exposure

8.7

7.9

8.3

8.4

9.2

9.1

8.2

8.1

8.9

8.2

8.9

7.5

After Exposure

9.4

9.8

9.9

10.3

8.9

8.8

9.8

8.2

9.4

9.9

12.2

9.3

  1. Is this independent or paired data and why
  2. Which nonparametric test would be appropriate to compare the two groups
  3. Test to determine if there is a difference in the distribution of lung capacity in rats before and after exposure. Use appropriate non parametric test.

     Alpha= 0.5


Answers


Answer Date: 25/01/2019 This is paired data due to each sample before exposure and after exposure is taken from single population. The Wilcoxon signed-rank nonparametric test is appropriate due the data is paired and alternative signed-rank test. To test the hypothesis is that there is a difference in the distribution of lung capacity in rats before and after exposure at 5% level of significance. The null and alternative hypothesis is, The Wilcoxon signed-rank test statistics is, First, compute the sum ofranks then find Wilcoxon signed-ranktest statistics. By using SPSS, find sum of ranks with the help of following steps 1) Import the Rank data and Sorce data by grouping.</p><p>2) Select 2 Related Samples Test from Nonparametric Test in Analyze option3) 4) Select Test Pairs Click Ok. Wilcoxon Signed Ranks Test Ranks Mean Rank Sum of Ranks 73.00 5.00 Before After Negative Ranks 7.30 2.50 10a Positive Ranks Ties Total 0c 12 a. Before < After b. Before > After c. Before After Test Statistics Before After 2.670a 008 Asymp.</p><p>Sig. (2-tailed)From the SPSS output, the sum of ranks positive is 5 and sum of ranks negative is 73 The Wilcoxon signed-rank test statistics is, T- Smaller group total (Positive or negative) - positive group total The Wilcoxon signed-rank test statistics is 5. The p-value for this test is, From the SPSS output, the p-value for this test is 0.008 Decision The conclusion is that p-value in this context is less than 0.05 which is 0.008, so the null hypothesis is rejected at 5% level of significance. There is sufficient evidence to indicate that there is a difference in the distribution of lung capacity in rats before and after exposure. The result is statistically significant.

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