Question

A loonie is flipped 36 times and 11 heads are observed. A toonie is flipped 100 times and 50 heads are observed. Let \pi x= p[getting heads of the loonie] and \pi y = p[getting heads of the toonie].

a) Find a 90% CI for \pi x - \pi y. The left endpoint of the interval is _____ and the right endpoint of the interval is _____.

b) If the following hypotheses are test:

Ho: \pi x- \pi y =0 Ha:\pi x- \pi y \neq 0

What is the conclusion? Reject or not

Answer 1

(A) Using the given data in question

px = x/n = 11/36

py = y/m = 50/100

z critical = 1.645 (using z table)

Confidence interval =

(B) We can see that the confidence interval has both limits below 0

This means that the lower limit and upper limit for the confidence interval for proportion difference are less than 0. So, this tells us that there is a significant difference between the proportion

therefore, we can reject the null hypothesis in this case as the confidence interval does not include 0