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Answer:
A) CI = (-0.1969, 0.0269)
B) There is no major difference between the two pieces of equipment because from the confidence interval we calculated earlier, we can see that it also includes 0. This implies that there is not a significant difference between the two provided proportions.
Step-by-step explanation:
A) We are dealing with service contract sold on treadmills versus service contracts sold on exercise bikes. Thus;
Sample proportion of service contract sold on treadmills is;
p1^ = 67/185
p1^ = 0.3622
Similarly, Sample proportion of service contract sold on exercise bikes is;
p2^ = 55/123
p2^ = 0.4472
Sample size of service contract sold on treadmills; n1 = 185
Sample size of service contract sold on exercise bikes; n2 = 123
Critical value at 95% significance level is; z = 1.96
Formula for confidence interval in this situation is;
CI = (p1^ - p2^) ± z√[(p1^(1 - p1^)/n1) + (p2^(1 - p2^)/n2)]
Plugging in the relevant values gives;
CI = (0.3622 - 0.4472) ± 1.96√[(0.3622(1 - 0.3622)/185) + (0.4472(1 - 0.4472)/123)]
CI = -0.085 ± 1.96√(0.00124870897 + 0.00201)
CI = -0.085 ± 1.96(0.05709)
CI = -0.085 ± 0.1119
CI = (-0.1969, 0.0269)
B) There is no major difference between the two pieces of equipment because from the confidence interval we calculated earlier, we can see that it also includes 0. This implies that there is not a significant difference between the two provided proportions.
