Question

The dataset flatulence.xlsx includes the variables gender, the self-reported number of times per day the respondent passes gas (perday), and the number of months the respondent claims to wait before passing gas in front of a romantic partner (howlong).

1. Find the 95% confidence interval for the average number of times a person passes gas in a day.
2. Find the 99% confidence interval for:
   1. the average number of months a female waits before passing gas in front of a romantic partner, and
   2. the average number of months a male waits before passing gas in front of a romantic partner.
   3. Compare the confidence intervals found above. Does this lead you to believe that there may be a difference between the number of months females and males wait before passing gas in front of a romantic partner? Why or why not?
3. Do the data provide enough evidence to conclude that the average number of times per day that males and females pass gas is different? Support your claim with a p-value.
4. Do the data provide enough evidence to conclude that the average number of months that males and females wait to pass gas in front of a romantic partner is different? Support your claim with a p-value

5. Gender	perday	howlong
   male	3	1,2
   male	5	12
   male	5	6
   male	2	36
   male	2	9
   male	5	12
   male	2	9
   male	2	6
   male	3	6
   male	6	6
   male	1	12
   male	4	6
   male	7	3
   male	2	1,2
   male	5	12
   male	1	6
   male	1	12
   female	3	24
   female	4	12
   female	12	6
   female	2	12
   female	2	6
   female	1	24
   female	12	1,2
   female	5	12
   female	3	6
   female	3	6
   female	6	6
   female	1	6
   female	3	3
   female	4	1,2
   female	3	12
   female	10	9
   female	0	12

Answer 1

• The 95% Confidence interval for the average number of times a person passes gas in a day is given by:
  
  
  where,
  
  n = 34
  
  
  
  Hence, the required CI is:
  
  
  
  
  
• In the howlong column of the data, many data-points are 1,2. I have changed them to 12, since, 1,2 doesn't make sense. If it is something else, please let me know, and I will do the necessary computation.
  
  The 99% confidence interval for the average number of months a female waits before passing gas in front of a romantic partner is given by:
  
  where,
  
  n = 34
  
  
  Hence, the required CI is:
  
  
  
  
  
  
• Proceeding in the same way the CI for Male is:
  
  
  
  
• On comparing the Confidence Intervals for male and female we observe that, the Confidence Intervals are not very different. Their boundaries are very close to each other.
  
  
  
• Here we are to test,
  
  
  We use the test statistic:
  
  
  Under Null,
  
  
  Now,
  
  
  
  p-value
  
  
  
  
  Hence, we conclude that, there is no difference between the average number of months that males and females wait to pass gas in front of a romantic partner.
  
  
  
  

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