Question

A confidence interval is constructed for an unknown population proportion, p. A sample is collected, and the 95% confidence interval is calculated to be 0.41 ± 0.05. Based on this information, it is most accurate to say that there is approximately 95% confidence in the assertion that:

a. the population proportion is between 0.36 and 0.46
b. the sample proportion is between 0.36 and 0.46
c. the sample proportion is 0.41
d.the population proportion is 0.41

Answer 1

Answer: a. the population proportion is between 0.36 and 0.46 .

Explanation:

Interpretation of 95% confidence interval : A person can be 95% confident that the true population parameter lies in 95% confidence interval.

Given : A 95% confidence interval for an unknown population proportion, p is calculated to be 0.41 ± 0.05.

i.e. Lower limit = 0.41-0.05 = 0.36

Upper limit = 0.41+0.05 = 0.46

Population parameter = p

Interpretation : A person can be 95% confident that the true population parameter lies between 0.36 and 0.46.

i.e. It is most accurate to say that there is approximately 95% confidence in the assertion that: the population proportion is between 0.36 and 0.46.