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Chapter 8: Q.8 (page 482)

Auto emissions Refer to Exercise 6. Below your sketch, choose one value of x inside the shaded region and draw its corresponding confidence interval. Do the same for one value of x outside the shaded region. What is the most important difference between these intervals? (Use Figure 8.5, on page 474, as a model for your drawing.)

Short Answer

Expert verified

The most important difference between these intervals

Step by step solution

01

Given Information

Model drawing:

02

Explanation

If the sample mean x¯lies in the shaded region, then the confidence interval will contain the true population mean μ.

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Most popular questions from this chapter

It’s critical Find the appropriate critical value for constructing a confidence interval in each of the following settings.

(a) Estimating a population proportion p at a 94%confidence level based on an SRS of size 125.

(b) Estimating a population mean M at a 99%confidence level based on an SRS of size 58.

61. Willows in Yellowstone Writers in some fields summarize data by giving x¯and its standard error rather than x¯and sx. Biologists studying willow trees in Yellowstone National Park reported their results in a table with columns labeled x¯+SE. The table entry for the heights of willow trees (in centimeters) in one region of the park was 61.55±19.03.The researchers measured a total of23 trees.
(a) Find the sample standard deviation sx for these measurements. Show your work.
(b) Explain why the given interval is not a confidence interval for the mean height of willow trees in this region of the park.

Interpret the confidence level.

In preparing to construct a one-samplet interval for a population mean, suppose we are not sure if the population distribution is Normal. In which of the following circumstances would we not be safe constructing the interval based on an SRS of size 24from the population?

(a) A stem plot of the data is roughly bell-shaped.

(b) A histogram of the data shows slight skewness.

(c) A stem plot of the data has a large outlier.

(d) The sample standard deviation is large.

(c) The tprocedures are robust, so it is always safe.

What critical value t⋆from Table B would you use for a 90%confidence interval for the population mean based on an SRS of size 77? If possible, use technology to find a more accurate value of t⋆. What advantage does the more accurate df provide?
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