Question

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? Do the data appear to be from a normally distributed population as​ required?

263, 206, 182, 168, 166, 153, 153, 153, 151, 148

$_ million < μ < $ _ million

round to one decimal place

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Xbar = 174.3

S = 35.95691867

n = 10

df = n – 1 = 9

Confidence level = 95%

Critical t value = 2.2622

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 174.3 ± 2.2622*35.95691867/sqrt(10)

Confidence interval = 174.3 ± 25.7220

Lower limit = 174.3 - 25.7220 = 148.58

Upper limit = 174.3 + 25.7220 = 200.02

Confidence interval = (148.6, 200.0)

$148.6 million < µ < $200.0 million