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

The 95% confidence interval is wider than the 90% confidence interval. The sample proportion and the population proportion may or may not lie within the confidence interval. The confidence interval provides an estimate, but does not represent a probability.

Step-by-step explanation:

The statement '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' is correct. This is because the higher the confidence level, the wider the confidence interval.

The statement 'The sample proportion must lie in the 95% confidence interval' is incorrect. The sample proportion may or may not lie in the confidence interval.

The statement 'There is a 95% chance that the 95% confidence interval actually contains the population proportion' is incorrect. The confidence interval provides an estimate of where the population parameter is likely to be, but it does not represent a probability.

The statement 'We don't know if the 95% confidence interval actually does or doesn't contain the population proportion' is correct. The confidence interval provides an estimate, but we cannot be certain if it contains the population proportion or not.

The statement 'The population proportion must lie in the 95% confidence interval' is incorrect. The population proportion may or may not lie in the confidence interval.

Answer 2

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.