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Chapter 7: Q5 (page 327)

Using Correct Distribution. In Exercises 5鈥�8, assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) Find the critical valuet伪2, (b) find the critical value z伪2, or (c) state that neither the normal distribution nor the t distribution applies.

Miami Heat Salaries Confidence level is 95%, 蟽is not known, and the normal quantile plot of the 17 salaries (thousands of dollars) of Miami Heat basketball players is as shown.

Short Answer

Expert verified

Neither the normal distribution nor the t distribution is applicable.

Step by step solution

01

Given information

A sample of salaries is of Miami Heat Basketball players is considered with a sample size of 17. A normal quantile plot is constructed for the values.

02

Appropriate method

The following points are used to decide the appropriate method for constructing the confidence interval estimate of the population mean:

  • Ifis unknown and the sample is either from a normally distributed population or the sample size is greater than 30, use the t-distributiont伪2
  • Ifis known and the sample is either from a normally distributed population or the sample size is greater than 30, use the standard normal distributionz伪2.
  • If the sample is not from a normally distributed population, do not use any of the above two distributions. Rather, use the bootstrap sampling method.
03

Interpretation of the normal quantile plot

It can be observed from the given graph that the points are not close to the straight line. This implies that the sample data are not from a normally distributed population. The distribution is skewed.

04

Deciding the correct distribution

Since the sample is not from a normally distributed population,neither the normal distribution nor the t distribution can be applied.

Thus, option (c) is correct.

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Most popular questions from this chapter

Celebrity Net Worth Listed below are the amounts of net worth (in millions of dollars) of these ten wealthiest celebrities: Tom Cruise, Will Smith, Robert De Niro, Drew Carey, George Clooney, John Travolta, Samuel L. Jackson, Larry King, Demi Moore, and Bruce Willis. Construct a 98% 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?

250 200 185 165 160 160 150 150 150 150

In Exercises 1鈥�3, refer to the accompanying screen display that results from the Verizon airport data speeds (Mbps) from Data Set 32 鈥淎irport Data Speeds鈥� in Appendix B. The confidence level of 95% was used

Airport Data Speeds Refer to the accompanying screen display.

a. Express the con铿乨ence interval in the format that uses the 鈥渓ess than鈥� symbol. Given that the original listed data use one decimal place, round the con铿乨ence interval limits accordingly.

b. Identify the best point estimate of and the margin of error.

c. In constructing the con铿乨ence interval estimate of , why is it not necessary to con铿乺m that the sample data appear to be from a population with a normal distribution?

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a.Construct a 95% confidence interval estimate of the percentageof OxyContin users who develop nausea.

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Critical ValueFor the survey described in Exercise 1 鈥淐elebrities and the Law,鈥� find the critical value that would be used for constructing a 99% confidence interval estimate of the population proportion.

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b. Are the survey results consistent with the actual voter turnout of 61%? Why or why not?
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