Question

Construct a 95 percent confidence interval for the difference between the proportions of service contracts sold on treadmills versus exercise bikes. Determine if there is or is not a major difference between the two pieces of equipment and provide a rationale for your response.

Answer 1

The question is not complete, so i have attached it.

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.