Question

Find the mean, standard deviation, 80%, 95%, and 99% confidence intervals, and margin of error for those intervals. Show all work.

$32,096	$29,716	$29,227	$27,209	$22,794	$19,306	$19,238	$19,164	18,994	$18,329
$17,978	$17,626	$16,823	$16,709	$15,967	$15,921	$15,908	$15,905	$15,638	$15,629
$14,414	$14,229	$14,137	$14,051	$13,907	$13,776	$13,281	$12,739	$12,300	$11,994
$11,262	$11,112	$10,984	$10,824	$10,823	$10,448	$10,081	$9,883	$9,668	$9,663
$9,337	$8,855	$8,741	$8,596	$8,385	$7,204	$7,072	$6,503	$5,653	$4,602

Answer 1

Using Excel's functions for mean( AVERAGE) and standard deviation (STDEV) we have

Mean= 14294 and S.D= 6104.73

The provided sample mean is Xˉ=14294 and the sample standard deviation is s=6104.73. The size of the sample is n=50 and the required confidence level is 80%.

The number of degrees of freedom are df=50−1=49, and the significance level is α=0.2.

Based on the provided information, the critical t-value for α=0.2 and df=49 degrees of freedom is tc =1.299

MARGIN OF ERROR FOR 80% CI

For 95% confidence interval

MARGIN OF ERROR FOR 95% CI

Based on the provided information, the critical t-value for α=0.05 and df=49 degrees of freedom is tc=2.01.

MARGIN OF ERROR=

FOR 99% CONFIDENCE INTERVAL

Based on the provided information, the critical t-value for α=0.01 and df=49 degrees of freedom is tc​=2.68.

MOE