Question

30 individuals were asked the following question: What is your favorite soft drink? The table below shows the results.

Names	How many times a week do you typically exercise?
1	Diet Coke
2	Diet Coke
3	Pepsi
4	Diet Pepsi
5	Sprite
6	Mountain Dew
7	Diet Coke
8	Coke Zero
9	Sprite
10	Fanta
11	Root Beer
12	Sierra Mist
13	Diet Coke
14	Diet Dr. Pepper
15	Pepsi
16	Diet Pepsi
17	Diet Coke
18	Root Beer
19	Diet Coke
20	Sierra Mist
21	Diet Coke
22	Mountain Dew
23	7 UP
24	Sprite
25	Diet Coke
26	Root Beer
27	Dr. Pepper
28	7UP
29	Diet Coke
30	Diet Coke

1. Calculate the sample proportion for individuals that answered “Diet Coke”. SHOW THE CALCULATION

2. Calculate the appropriate SE based on the 30 individuals and #1 above. SHOW THE CALCULATION.

3. Calculate a 95% confidence interval for the proportion associated with the individuals who answered “Diet Coke”. SHOW ALL CALCULATIONS.

4. Interpret the full meaning of the confidence interval you have in #3. Remember to include all four components to an interpretation.

Answer 1

1. The sample proportion for individuals that answered “Diet Coke” = 10/30 = 0.33

2. SE = √p(1-p)/n = √0.33(1-0.33)/30 = 0.086

3. The 95% confidence interval will be:

= p ± z*(√p(1-p)/n

= 0.33 ± 1.96*(√0.33(1-0.33)/30

= (0.1646, 0.502)

4. We are 95% confident that the true proportion associated with the individuals who answered “Diet Coke” is between 0.1646 and 0.502.

Please give me a thumbs-up if this helps you out. Thank you!