Question

5 multiple answer 1 point select all that apply. if a 95% confidence level is selected, then 5 chances out of 100 will fall in the interval. there is a 5% chance of the interval being incorrect. the corresponding z score is 2.58. the probability of a selected sample falling in this interval is 0.95.

Explanation:

Step1: Analyze the first option

A 95% confidence level means 95 out of 100 intervals (not 5) will contain the True population parameter. So, "5 chances out of 100 will fall in the interval" is incorrect.

Step2: Analyze the second option

Confidence level \(C = 95\%=0.95\). The significance level \(\alpha=1 - C=1 - 0.95 = 0.05 = 5\%\). \(\alpha\) is the probability that the interval is incorrect. So, "there is a 5% chance of the interval being incorrect" is correct.

Step3: Analyze the third option

For a 95% confidence level, the \(z\) - score (critical value) is \(z_{\alpha/2}\), where \(\alpha = 0.05\) and \(\alpha/2=0.025\). From the standard normal table, \(z_{0.025}=1.96\) (not \(2.58\), which is for a 99% confidence level, \(\alpha = 0.01\) and \(\alpha/2 = 0.005\)). So, "the corresponding \(Z\) score is \(2.58\)" is incorrect.

Step4: Analyze the fourth option

By the definition of confidence level, if we construct many intervals, about 95% of them will contain the True population parameter. So, "the probability of a selected sample falling in this interval is \(0.95\)" is correct.

Answer:

B. there is a 5% chance of the interval being incorrect, D. the probability of a selected sample falling in this interval is 0.95.