Answered

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 :

Answer:

Upper confidence level (UCL) = 29367.875

Lower confidence level (LCL) =23061.064

Step-by-step 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 = [tex]\left( \bar{X} \pm t_{\frac{\alpha}{2}} \times  \frac{s}{\sqrt{n}} \right)[/tex]

sample mean= [tex]\bar{x}[/tex] =26214.47

sample standard deviation = s =5969.25

sample size = n =15

t critical value for 94% confidence with 14 degree of freedom [tex]t_{\frac{\alpha}{2}}[/tex]=2.046

Substitute the values in the formula :

confidence interval = [tex]26214.47 \pm 2.046 \times  \frac{5969.25}{\sqrt{15}}[/tex]

confidence interval = [tex]26214.47 - 2.046 \times  \frac{5969.25}{\sqrt{15}}[/tex] to [tex]26214.47 + 2.046 \times  \frac{5969.25}{\sqrt{15}}[/tex]

confidence interval = [tex]23061.064[/tex] to [tex]29367.875[/tex]

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

Other Questions