Question

Use the table below to answer questions 4.5 – 4.7: This table contains the same client data as the first table. This time, though, the instructor is interested in knowing how his clients’ other activities might impact their average cycling speed in spin class. He notes that half of his clients also ride bikes outside during the week, while the other half of his clients do not bike anywhere except spin class.

Rides Outside	Only Spin	Rides Outside	Only SPin	Rides outside	only spin
20	15
17	17
18	19
22	17
21	17
18	16
17	18

Average Speed M = 19 M = 17

4.5 Calculate SS for each sample of spin class clients (the portion who ride outside and the portion who only do spin class). Show Work by inserting numbers into the table to show intermediate steps Rides Outside SS = Only Spin Class SS =

4.6 Calculate s for each group Rides Outside s = Only Spin Class s =

4.7 Based on the statistics you have computed, does there appear to be any difference in average speed between those who bike outside and those who only bike during spin class?

Explain why or why not?

Answer 1

4.5) SS for rides outside and ss for only spin.

Rides Outside	Only Spin	SS for Rides Outside	SS for Only SPin
20	15	400	225
17	17	289	289
18	19	324	361
22	17	484	289
21	17	441	289
18	16	324	256
17	18	289	324
		2551	2033

4.6) S for rides outside and S for only spin

s for rides outside	s for only spin
2	1.290994449

4.7) Here the mean of rides outside is 19 and mean for only spin is17 and corresponding standard deviations are 2 and 1.29 respectively. To test whether these two means are statistically equal we use two sample t-test and the output is given below.

t-Test: Two-Sample Assuming Unequal Variances
	Rides Outside	Only Spin
Mean	19	17
Variance	4	1.666667
Observations	7	7
Hypothesized Mean Difference	0
df	10
t Stat	2.222875721
P(T<=t) one-tail	0.025224041
t Critical one-tail	1.812461102
P(T<=t) two-tail	0.050448083
t Critical two-tail	2.228138842

From above test it is clear that the means of two groups are not equal.