Question

A cycling colleague of mine recently complained to me about the “reckless” skateboarders on campus. I replied by noting that I’ve observed cyclists on campus to be far less respectful of pedestrians’ safety & space than are skateboarders. My colleague was quite upset with my response, so we set about testing whether there is any difference between skateboarders’ and cyclists’ regard for pedestrians on campus. My colleague and I observed the behavior of both skaters (n=43) and cyclists (n=50) in several areas on campus. We recorded the following data pertaining to “how respectful” skaters and cyclists passed pedestrians:

Skateboarders Bicyclist

Direspectful pass 26 42

Respectful Pass 17 8

43 50

1. Calculate and contrast appropriate percentages to determine if the courtesy demonstrated to pedestrians appears to differ between skateboarders and bicyclists on campus.

2. State Null Hypotheses

3. Set the critical value for the Chi-square test using a .01 alpha level

4. Calculate the obtained Chi-square value.

5. Interpret the results of your Chi-square test

Answer 1

1.

		Skateboarders	Bicyclist	Total
Direspectful pass	Observed	26	42	68
	% of total	28.0%	45.2%	73.1%
Respectful pass	Observed	17	8	25
	% of total	18.3%	8.6%	26.9%
Total	Observed	43	50	93
	% of total	46.2%	53.8%	100.0%

2. The hypothesis being tested is:

H0: The courtesy demonstrated to pedestrians does not appear to differ between skateboarders and bicyclists on campus

Ha: The courtesy demonstrated to pedestrians appears to differ between skateboarders and bicyclists on campus

3. 6.63

4. 6.51

5. Since 6.51 < 6.63, we fail to reject the null hypothesis.

Therefore, we cannot conclude that the courtesy demonstrated to pedestrians appears to differ between skateboarders and bicyclists on campus.

		Skateboarders	Bicyclist	Total
Direspectful pass	Observed	26	42	68
	Expected	31.44	36.56	68.00
	O - E	-5.44	5.44	0.00
	(O - E)² / E	0.94	0.81	1.75
Respectful pass	Observed	17	8	25
	Expected	11.56	13.44	25.00
	O - E	5.44	-5.44	0.00
	(O - E)² / E	2.56	2.20	4.76
Total	Observed	43	50	93
	Expected	43.00	50.00	93.00
	O - E	0.00	0.00	0.00
	(O - E)² / E	3.50	3.01	6.51
		6.63	critical
		6.51	chi-square
		1	df
		.0107	p-value

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