Question

How much money do winners go home with from the television quiz show Jeopardy? 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. sample mean=26214.47, sample standard deviation=5969.25, sample size=15, degree of freedom=14, t critical value for 94% confidence with 14 degree of freedom=2.046

Upper confidence level (UCL) =?Lower confidence level (LCL) =?

Answer 1

Upper confidence level (UCL) = 29367.875

Lower confidence level (LCL) =23061.064

Explanation:

Given : sample mean=26214.47

sample standard deviation=5969.25

sample size=15

degree of freedom=14

t critical value for 94% confidence with 14 degree of freedom=2.046

To Find : Upper confidence level (UCL) =?Lower confidence level (LCL) =?

Solution:

Formula for confidence interval =
`\left( \bar{X} \pm t_{(\alpha)/(2)} *  (s)/(√(n)) \right)`

sample mean=
`\bar{x}` =26214.47

sample standard deviation = s =5969.25

sample size = n =15

t critical value for 94% confidence with 14 degree of freedom
`t_{(\alpha)/(2)}`=2.046

Substitute the values in the formula :

confidence interval =
`26214.47 \pm 2.046 *  (5969.25)/(√(15))`

confidence interval =
`26214.47 - 2.046 *  (5969.25)/(√(15))` to
`26214.47 + 2.046 *  (5969.25)/(√(15))`

confidence interval =
`23061.064` to
`29367.875`

Hence Upper confidence level (UCL) = 29367.875 and Lower confidence level (LCL) =23061.064