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Chapter 8: Q 8.11RP. (page 347)

The following figure shows the standard normal curve and two \(t\)-curves. Which of the two \(t\)-curves has the larger degrees of freedom? Explain your answer.

Short Answer

Expert verified

The t-curve which is closer to the standard normal curve has the larger degree of freedom.

Step by step solution

01

Given information

02

Explanation

The shape of the t-curve approaches the shape of a conventional normal curve as the number of degrees of freedom grows. As a result, the t-curve with the most degrees of freedom is closer to the conventional normal curve.

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Most popular questions from this chapter

Digital Viewing Times. Refer to Exercise 8.130

a. Find and interpret a 90%lower confidence bound for last year's mean time spent per day with digital media by American adults.

b. Compare your one-sided confidence interval in part (a) to the (two-sided) confidence interval found in Exercise 8.130.

Prices of New Mobile Homes. Recall that a simple random sample of 36 new mobile homes yielded the prices, in thousands of dollars, shown in Table 8.1on page 315 . We found the mean of those prices to be \(63.28thousand.

a. Use this information and Procedure 8.1on page 322 to find a 95%confidence interval for the mean price of all new mobile homes. Recall that 蟽=\)7.2thousand.

b. Compare your 95%confidence interval in part (a) to the one found in Example 8.2(c) on page 317 and explain any discrepancy that you observe.

Christmas Spending. In a national poll of 1039 U.S. adults, conducted November7-10,2013, Gallup asked "Roughly how much money do you think you personally will spend on Christmas gifts this year?". The data provided on the Weiss Stats site are based on the results of the poll.

a. Determine a 95% upper confidence bound for the mean amount spent on Christmas gifts in 2013 (Note: The sample mean and sample standard deviation of the data are \(704.00 and \)477.98, respectively.)

b. Interpret your result in part (a).

c. In 2012 , the mean amount spent on Christmas gifts was $770. Comment on this information in view of your answer to part (b).

American Alligators. Refer to Exercise 8.78.

a. Determine the margin of error for the 95%confidence interval.

b. Determine the margin of error for the 99%confidence interval.

c. Compare the margins of error found in parts (a) and (b).

d. What principle is being illustrated?

The margin of error is also called the maximum error of the estimate. Explain why.
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