  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

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

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)”

Step 3

Computation of 95% confidence interval:

95% confidence interval of the mean ...

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Advanced Topics in Statistics 