Question

The American Heart Association is a charitable organization that relies on donations. They send return address labels to potential donors on their list and ask for voluntary contributions. The organization designed a new address label and wants to determine the proportion of possible donors that will send a donation for these new labels. They mailed letters to a random sample of 1000 potential donors and received 37 donations. A staff member thinks the true proportion of possible donors is 4%. Given the confidence interval you found, do you think that percentage is plausible? Explain your reasoning.

Answer 1

Solution:

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 = 37

n = 1000

P = x/n = 37/1000 = 0.037

Confidence level = 95%

Critical Z value = 1.96

(by using z-table)

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

Confidence Interval = 0.037 ± 1.96* sqrt(0.037*(1 – 0.037)/ 1000)

Confidence Interval = 0.037 ± 1.96*0.0060

Confidence Interval = 0.037 ± 0.0117

Lower limit = 0.037 - 0.0117 = 0.0253

Upper limit = 0.037 + 0.0117 = 0.0487

Confidence interval = (0.0253, 0.0487)

The above confidence interval contains the true proportion of possible donors as 4% or 0.04, so this percentage is plausible.