Question

One of the hot topics in the last presidential election was with respect to our citizen’s health and whether or not the government has a right to limit our choices in what we eat or drink. A random sample of 1046 Americans was obtained. The question asked was “Do you support our govern-ment banning specific types or sizes of food or drinks?” Of those surveyed, 895 responded, “no.”

a. Estimate with 95% confidence the proportion of Americans who do not support the govern-ment banning specific types or sizes of food or drinks.

b. Using the confidence interval found in part a, can you conclude that a majority of Americans do not support the government banning specific types or sizes of food or drinks. Why or why not

Answer 1

Part a

Confidence interval for Population Proportion is given as below:

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Where, P is the sample proportion, Z is critical value, and n is sample size.

We are given

x = 895

n = 1046

P = x/n = 895/1046 = 0.855640535

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

Confidence Interval = P ± Z* sqrt(P*(1 – P)/n)

Confidence Interval = .855640535 ± 1.96* sqrt(.855640535*(1 – .855640535)/1046)

Confidence Interval = .855640535 ± 1.96* 0.0109

Confidence Interval = .855640535 ± 0.0213

Lower limit = .855640535 - 0.0213 = 0.8343

Upper limit = .855640535 + 0.0213 = 0.8769

Confidence interval = (0.8343, 0.8769)

Part b

Yes, we can conclude that a majority of Americans do not support the government banning specific types of sizes of food or drinks, because this interval contains values more than 0.5.