Question

Two different simple random samples are drawn from two different populations. The first sample consists of

2020

people with

1111

having a common attribute. The second sample consists of

22002200

people with

15801580

of them having the same common attribute. Compare the results from a hypothesis test of

p 1p1equals=p 2p2

​(with a

0.050.05

significance​level) and a

9595​%

confidence interval estimate of

p 1p1minus−p 2p2.

Answer 1

Using TI 84 calculator

press stat then tests then 1-propZTest

x1 = 11, n1 = 20

x2 = 1580, n2 = 2200

p1 not equals to p2

press ENTER

test statistic =-1.66

p value = 0.0966

Confidence interval result

Using TI 84 calculator

press stat then tests then 1-propZInt

x1 = 11, n1 = 20

x2 = 1580, n2 = 2200

c-level = 0.95

press ENTER

-0.387<p1-p2< 0.051

We can see that p value is greater than significance level of 0.05, shows that there is no significant difference between proportions

Confidence interval includes negative and positive values, means that the confidence interval includes 0. So, confidence interval also suggets that there is no difference between proportions