Listed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a
99%
confidence interval. What does the result tell us about the population of all celebrities? Do the data appear to be from a normally distributed population as required?
266 |
192 |
190 |
167 |
159 |
154 |
154 |
154 |
152 |
149 |
What is the confidence interval estimate of the population mean
muμ?
$nothing
millionless than<muμless than<$nothing
million
(Round to one decimal place as needed.)
Solution:
Confidence interval = Xbar ± t*S/sqrt(n)
From given data, we have
Xbar = 173.7
S = 35.94146476
n = 10
df = n – 1 = 10 – 1 = 9
confidence level = 99%
Critical t value = 3.2498
(by using t-table)
Confidence interval = 173.7 ± 3.2498*35.94146476/sqrt(10)
Confidence interval = 173.7 ± 3.2498* 11.36568911
Confidence interval = 173.7 ± 36.9366
Lower limit = 173.7 - 36.9366 = 136.76
Upper limit = 173.7 + 36.9366 = 210.64
$136.8 million < µ < $210.6 million
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