Question

A gym offers a routine of intensive Zumba classes during the first 3 days of registration, a sample of 10 new members was obtained and the data of the participation time were taken. The data was 12, 17, 19, 10 18, 17, 23, 13, 16, 18. Find a confidence interval for the proportion of new partners who exercised for more than 17 minutes with a 3% significance level.

Answer 1

There are 4 entries who exercised for more than 17 minutes.

the proportion of new partners who exercised for more than 17 minute = $\widehat{p}=\frac{4}{10}=0.4$

3% significance level means 97%confidence

The sample proportion is computed as follows, based on the sample size N = 10 and the number of favorable cases X = 4: X P N 0.4 10 The critical value for a = 0.03 is ze = 71-a/2 = 2.17. The corresponding confidence interval is computed as shown below: CI(Proportion) p(1-P) p(1-P) 0 P + c n 0.4 - 2.17 x V 0.4(1 -0.4) ,0.4 +2.17 x 10 0.4(1 -0.4) 10 (0.064, 0.736)