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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 money won by those winners is listed below. Construct a 95% confidence interval to estimate the mean winnings for all players on Jeopardy.$26,650      $6,060            $52,820     $8,490      $13,660$25,840      $49,840         $23,790     $51,480     $18,960$990           $11,450           $41,810       $21,060     $7,860

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 money won by those winners is listed below. Construct a 95% confidence interval to estimate the mean winnings for all players on Jeopardy.

$26,650      $6,060            $52,820     $8,490      $13,660

$25,840      $49,840         $23,790     $51,480     $18,960

$990           $11,450           $41,810       $21,060     $7,860

check_circleAnswer
Step 1

Solution:

Confidence interval formula:

Confidence interval = sample statistic ± margin of error

Where, margin of error = critical value × standard error of statistic.

For n < 30, the confidence interval is shown as follows

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Step 2

Computation of alpha:

Here, confidence level is 95%.

α = 1−0.95

   = 0.05

Critical Probability:

p = 1− α/2

   = 1−(0.05/2)

   = 0.975

Degrees of freedom:

df = n−1

    = 15−1

    = 14

Sample Mean:

The average money won by 15 winners is 24,050.67 using the EXCEL formula, “=AVERAGE(A1:A15)”.

Sample standard deviation:

The sample standard deviation is 17,386.13 using the EXCEL formula, “=STDEV.S(A1:A15)”

Computation of Margin of error:

Critical value is 2.1448 using the EXCEL formula, “=T.INV(0.975,14)”

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Step 3

Computation of 95% confidence interval:

95% confidence interval of the mean ...

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