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?

 

260 206 199 156 155 153 147 147 147 147 

 

What is the confidence interval estimate of the population mean μ? 

Answer 1

Concepts and reason

The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter, assuming that a large number of samples are selected and the estimation process on the sample parameter is repeated.

A confidence interval is a specific interval estimate of a parameter determined by using data obtained from a sample and by using the specific confidence level of the estimate.

The margin of error is the maximum likely difference between the point estimate of a parameter and the actual value of the parameter.

Fundamentals

The formula for confidence interval for the mean when unknown is,

Here,

Number of sample values.

Sample standard deviation

Margin of error

Critical values

The values of sample mean and sample standard deviation are,

The degree of freedom is,

Critical value:

Using the t-distribution tables, the critical value at 5% level of significance with degree of freedom (9) is,

Substitute the values in the formula of confidence interval as follows:

Interpretation:

One can be 95% confident that the true population mean is lies between 144.5 and 198.9.

The data does not tell anything about the population of celebrities.

From step (2), the 95% confident that the true population mean is lies between 144.5 and 198.9.

The results tell nothing about the population of all celebrities.

Use the Minitab instructions to construct the normal probability plot as follows:

• Enter the data in the Minitab work sheet.

• Select graph from the Minitab too bar.

• Choose single plot from the probability plot.

• In the probability plot dialog box, shift the variable amount of net worth in to the graph variable.

• Click ok.

The output shows the normal probability plot for the given data.

From the plot, it can be observed that data does not appear to be normally distributed population.

Ans:

The 95% confident that the true population mean is

The results tell nothing about the population of all celebrities, because the amounts of net worth of the celebrities are not a representative sample, this does not provide information about the population of all celebrities.

No, because the points lie reasonable close to a straight line but there is a systematic pattern that is not a straight line pattern.