assume that population means are to be estimated from the sa

assume that population means are to be estimated from the samples described. use the sample results to approximate the margin of error of 95% confidence interval. sample size=1078, sample mean=$46,196, sample standard deviation=$21,000

find the 95% confidence interval

Solution

To construct 95% cofidence interval for p with margin of error equal to 95%,steps to be considered are:

As p is unknown,assume p=0.5

For a 95% confidence interval z^*=1.96

since,s=21000,n=1078, SEM=21000/V^---1078=21000/32.83=639.65

since,sample mean=46,196 and margin of error is 95%, z^*=1.96

so, confidence interval for 95% is,

$46196+1.96(639.65)=$46196+1253.71

=$47449.71