A 95% confidence interval for a population proportion was constructed using a sample proportion from a random sample. Which of t
he 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.
<em>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.</em>
True. Confidence interval gets wider as the confidence level decreases.
<em>The sample proportion must lie in the 95% confidence interval. </em>
True. Confidence interval is constructed around sample mean.
<em>There is a 95% chance that the 95% confidence interval actually contains the population proportion.</em>
True. Constructing 95%. confidence interval for a population proportion using a sample proportion from a random sample means the same as the above statement.
<em>We don't know if the 95% confidence interval actually does or doesn't contain the population proportion</em>
True. There is 95% chance that confidence interval contains population proportion and 5% chance that it does not.
<em>The population proportion must lie in the 95% confidence interval</em>
False. There is 95% chance that population proportion lies in the confidence interval.
