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 0.40 ± 0.06. Based on this information, it is most accurate to say that there is approximately 95% confidence in the assertion that:

Answer 1

Answer: The population proportion is between 0.34 and 0.46 .

Explanation:

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

A confidence interval is constructed for an unknown population proportion, p. A sample is collected, and the 95% confidence interval is calculated to be 0.40 ± 0.06.

i.e. Lower limit =
`0.40-0.06=0.34`

Upper limit =
`0.40+0.06=0.46`

i.e. 95% confidence interval = (0.34, 0.46)

i.e. A person can be about 95% confident that the true population proportion (p) lies in the interval (0.34, 0.46).

⇒ It is most accurate to say that there is approximately 95% confidence in the assertion that:

The population proportion is between 0.34 and 0.46 .