Question

A 95% confidence interval for a population proportion was constructed using a sample proportion from a random sample. Which of the following statements are correct? Select all that apply. If we were to use a 90% confidence level, the confidence interval from the same data would produce an interval wider than the 95% confidence interval. The sample proportion must lie in the 95% confidence interval. There is a 95% chance that the 95% confidence interval actually contains the population proportion. We don't know if the 95% confidence interval actually does or doesn't contain the population proportion. The population proportion must lie in the 95% confidence interval.

Answer 1

Answer:

All but last statement are correct.

Step-by-step explanation:

• If we were to use a 90% confidence level, the confidence interval from the same data would produce an interval wider than the 95% confidence interval.

True. Confidence interval gets wider as the confidence level decreases.  

• The sample proportion must lie in the 95% confidence interval.

True. Confidence interval is constructed around sample mean.

• There is a 95% chance that the 95% confidence interval actually contains the population proportion.

True. Constructing 95%. confidence interval for a population proportion using a sample proportion from a random sample means the same as the above statement.

• We don't know if the 95% confidence interval actually does or doesn't contain the population proportion

True. There is 95% chance that confidence interval contains population proportion and 5% chance that it does not.

• The population proportion must lie in the 95% confidence interval

False. There is 95% chance that population proportion lies in the confidence interval.