Total sold 185 123 308
contract 67 55 122
Total 252 178
The confidence interval (C.I) for the difference in proportion is obtained using the formula:
C.I diff = , where , and
The proportion of service contract sold on the treadmill is 67/122, whereas the proportion of
those sold the exercise bike is 55/122. Therefore, to construct the confidence interval we need
p1, p2, n1, n2, standard error of the difference, and the z α .
Thus, let p 1 = 67/122, n 1 = 122, and p 2 = 55/122, n 2 = 122
D = =
SE p1 – p 2 =
CI = .
Key to note, the confidence interval is as effective as the test of hypothesis (ANOVA or T-
test), for it can be used in determining whether two averages or proportions are statistically
significant. The constructed confidence interval implies that we are 95% confident that the
proportion difference will lie between -0.0265, and 0.2232. Notably, the constructed
confidence interval contains zero, which means that the difference between the proportion of
service contract sold on the treadmill and the proportion of those sold on the exercise bike is
not significantly different from zero. In other words, the two sales are not statistically
different at the 95% level of significance. In simple terms, this deduces that in the past six
months, the Service contract sold using the treadmill and exercise bike was not significantly
different. That is to say, the two channels of distributions are equally effective in the sale of
the service contract. Therefore, when the firm is advertising, they need to emphasize about
the two selling techniques equally.
Samuels, M. L., Witmer, J. A., & Schaffner, A. (2012). Statistics for the life sciences.