Answer:
The confidence interval for 90% confidence would be narrower than the 95% confidence
Step-by-step explanation:
From the question we are told that
The sample size is n = 41
For a 95% confidence the level of significance is and
the critical value of is
For a 90% confidence the level of significance is and
the critical value of is
So we see with decreasing confidence level the critical value decrease
Now the margin of error is mathematically represented as
given that other values are constant and only is varying we have that
Hence for reducing confidence level the margin of error will be reducing
The confidence interval is mathematically represented as
Now looking at the above formula and information that we have deduced so far we can infer that as the confidence level reduces , the critical value reduces, the margin of error reduces and the confidence interval becomes narrower
