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

Question

Scarlet Levy

Mathematics

30 October, 02:01

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

+1

Answers (1)

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Bryant Liu · Answer 1

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

Step-by-step 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.