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 7.53

7.53 Noise levels in fitness classes.

Fitness classes often have very loud music that could affect hearing. One study collected noise levels (decibels) in both high-intensity and low-intensity fitness classes across eight commercial gyms in Sydney, Australia.27

noise

  1. Create a histogram or Normal quantile plot for the high-intensity classes. Do the same for the low-intensity classes. Are the distributions reasonably Normal? Summarize the distributions in words.
  2. Test the equality of means using a two-sided alternative hypothesis and significance level .
  3. Are the procedures appropriate given your observations in part (a)? Explain your answer.
  4. Remove the one low decibel reading for the low-intensity group and redo the significance test. How does this outlier affect the results?
  5. Do you think the results of the significance test from part (b) or (d) should be reported? Explain your answer.

7.53

(a) Both distributions are Normally distributed, except the low-intensity class has a low outlier.
(b) . The data are significant at the 5% level, and there is evidence the noise levels are different between the high- and low-intensity fitness classes. (c) Because the low-intensity class has an outlier, the -test is not appropriate. (d) . Removing the outlier didn’t change the results. (e) Because the outlier is not affecting the results, it is probably okay to report both tests. It would be a good idea to investigate the outlier and see why it had such a low decibel value; if it were drastically different in some way, it might be good to remove it and only report the test without it after mentioning its removal.