Use the table below to answer questions 4.5 – 4.7: This table contains the same
ID: 3072760 • Letter: U
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
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?
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 18Explanation / Answer
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.
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
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