Question

Part B, X=750, n=1000, confidence interval 95% with 5,000 samples - lower bound at 0.722 and upper bound at 0.776. Part C x=750, n=1000 confidence interval 99% with 5,000 samples - lower bound is 0.715 and upper bound is 0.785, standard error for both is 0.14.

In parts B and C the samples were the same by the confidence level changed. How did the confidence interval change when the confidence level was increased? Explain why?

Answer 1

Confidence interval is given by the equation C.I

C.I=$\overline{X}\pm Z_{\alpha /2}\frac{\sigma }{\sqrt{n}}$

Where $\overline{X}=Mean$

$\sigma =Standard deviation$

$n=number of sample$

when confidence level will be increased Value of $Z_{\alpha /2}$ will also be increased which will cause the increase in the range of confidence interval

That's  why Confidence interval changed when confidence level is changed

For example

99% Confidence interval has the Z value of 2.58

while 95% Confidence interval has Z value of 1.96