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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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