8. Construct the indicated confidence interval for thepopulation mean using (a)

Question

8. Construct the indicated confidence interval for thepopulation mean using (a) a t-distribution. (b) If you hadincorrectly used a normal distribution, which interval would bewider? (a) The 95% confidence interval using a t-distribution is(____-____). (b) If you had incorrectly used a normal distribution, whichinterval would be wider? The t-distribution has the wider interval. or The normal distribution has the wider interval. 8. Construct the indicated confidence interval for thepopulation mean using (a) a t-distribution. (b) If you hadincorrectly used a normal distribution, which interval would bewider? (a) The 95% confidence interval using a t-distribution is(____-____). (b) If you had incorrectly used a normal distribution, whichinterval would be wider? The t-distribution has the wider interval. or The normal distribution has the wider interval.

Explanation / Answer

(a) we take the following example: at c=0.95 i.e =0.05 for a two tail distribution and df= n-1 = 15-1 = 14, t =2.145         (from ttable) x(with a line on top of the x)=112 s=10 n=15. standard error, e = s / n = 10/15 = 2.582 A 95% confidence interval for = x ± (t*e) =112 ± (2.145*2.582) = (106.462, 117.54) (b) If we hadincorrectly used a normal distribution, then at c=0.95 i.e =0.05 for a two tail distribution , z =1.96 A 95% confidenceinterval for = x ± (z*e) =112 ±(1.96*2.582) = (106.94, 117.061) hence we can seethat  t-distribution has the widerinterval (b) If we hadincorrectly used a normal distribution, then at c=0.95 i.e =0.05 for a two tail distribution , z =1.96 A 95% confidenceinterval for = x ± (z*e) =112 ±(1.96*2.582) = (106.94, 117.061) hence we can seethat  t-distribution has the widerinterval hence we can seethat  t-distribution has the widerinterval

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