Question

Question: I had a group project for my class where we asked 45 people if they preferred bottled or tap water. Results were: 11 preferred tap, 34 preferred bottled

Margin of Error was:

H0: P1 = P2 (CLAIM)

HA: P1 ? P2

(Our hypothesis claimed that there was no difference in taste, people preferred each one equally)

How would I go about constructing AND graphing a confidence interval and finding the standard deviation for my results? I'm confused.

Answer 1

Let p denotes the true proportion of people who preferred tap water.

To test whether there was no difference in taste, people preferred each one equally,

i.e. to test against

Here

sample proportion of people who preferred tap water

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 5% level of significance if P-value < 0.05

Now,

The value of the test statistic

P-value

Since P-value < 0.05, so we reject H₀ at 5% level of significance and we can conclude that there was significant difference in taste.