High School

Listed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a 95% confidence interval. What does the result tell us about the population of all celebrities?

155, 153, 147, 147, 147, 147, 260, 206, 199, 156

What is the confidence interval estimate of the population mean [tex]\mu[/tex]?

$_________ million to $_________ million

(Round to one decimal place as needed.)

Answer :

The 95% confidence interval estimate of the population mean net worth of all celebrities is approximately $142 million to $191.40 million.

What's the value?

Sample mean

(155 + 153 + 147 + 147 + 147 + 147 + 260 + 206 + 199 + 156) / 10 = 1667 / 10 = 166.7

Sample standard deviation (s):

[(155 - 166.7)² + (153 - 166.7)² + (147 - 166.7)² + (147 - 166.7)² + (147 - 166.7)² + (147 - 166.7)² + (260 - 166.7)² + (206 - 166.7)² + (199 - 166.7)² + (156 - 166.7)²] / (10 - 1) = 10944.3 / 9 ≈ 1216.03

s ≈ √1216.03 ≈ 34.89

Calculate the margin of error (MOE) using the formula:

MOE = (t-score) * (s / √n)

MOE = 2.2622 * (34.89 / √10) ≈ 24.70

Finally, construct the 95% confidence interval:

Confidence Interval = (x - MOE, x + MOE)

Confidence Interval = (166.7 - 24.70, 166.7 + 24.70)

Confidence Interval ≈ (142.00, 191.40)

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