How much money do winners go home with from the television q

How much money do winners go home with from the television quiz showJeopardy? To determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. Estimate with 96% confidence the mean winning\'s for all the show\'s players. (You may assume a normally distributed population.)

35766, 41253, 40622, 34487, 33624, 35237, 37348, 35967, 36475, 46774, 34234, 44978, 31009, 35192, 46407

Please give steps to solve confidence interval (and you are most likely to use t* in solving the problem)

Solution

sample size= n=15

sample mean =37958.2

sample standard deviation =4896.973

The degree of freedom =n-1=15-1=14

Given a=1-0.96= 0.04 , t(0.02, df=14) =2.26 (from student t table)

So the lower bound is

xbar - t*s/vn =37958.2 - 2.26*4896.973/sqrt(15) =35100.67

So the upper bound is

xbar + t*s/vn=37958.2 + 2.26*4896.973/sqrt(15) =40815.73