Question

Suppose you are a researcher in a Starbucks Coffee Store. Recall that 20 of 33 people who interested in cold coffee than the hot ones. Thus a 60% confidence interval for the proportion of people who were coming to the store the same day. Find CI, point estimate and which distribution should you use for this problem?

Answer 1

Solution :

Z distribution used for this prolem .

n = 33

x = 20

Point estimate = = x / n = 20 / 33 = 0.606

1 - = 1 - 0.606 = 0.394

At 60% confidence level the z is ,

= 1 - 60% = 1 - 0.60 = 0.40

/ 2 = 0.40 / 2 = 0.20

Z_/2 = Z_0.20 = 0.84

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 0.84 * (((0.606 * 0.394) / 33)

= 0.072

A 60% confidence interval for population proportion p is ,

- E < P < + E

0.606 - 0.072 < p < 0.606 + 0.072

0.534 < p < 0.678

(0.534 , 0.678)