Question

Listed below are the amounts of net worth (in millions of dollars) of the ten wealthiest celebrities in a country. Construct a 90% 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? 241, 195, 188,171,164,154,151,151,151,146 What is the confidence interval estimate of the population mean u?

$ __ million< u <$__ milion

round to one decimal place as needed

Answer 1

Solution :

Given that,

From the data,

241, 195, 188,171,164,154,151,151,151,146

Mean :

= (X) / n

= 1712 / 10 = 171.2

Variance :

s = ( X - )² / n - 1

= 880.84 = 29.7

Point estimate = sample mean = = 171.2

sample standard deviation = s = 29.7

sample size = n = 10

Degrees of freedom = df = n - 1 = 9

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,24 = 1.833

Margin of error = E = t_/2,df * (s /n)

= 1.833 * ( 29.7/ 10)

= 17.2

The 90% confidence interval estimate of the population mean is,

- E < < + E

171.2 - 17.2 < < 171.2 + 17.2

154.0 < < 188.6