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Chapter 8: Q 8.8RP. (page 346)

Suppose that you plan to apply the one-mean z-interval procedure to obtain a 90%confidence interval for a population mean, μYou know that σ=12 and that you are going to use a sample of size 9

a. What will be your margin of error?

b. What else do you need to know in order to obtain the confidence interval?

Short Answer

Expert verified

Part (a)6.5794

Part (b)(x¯-E,x¯+E)

Step by step solution

01

Part (a) Step 1: Given information

Population s.d.σ=12

Sample size n=9

02

Part (a) Step 2: Concept

The formula used:E=Zα/2×σn

03

Part (a) Step 3: Calculation

Population s.d.σ=12

Sample size n=9

Confidence level =90%=100×0.90%

∴1-α=0.90⇒α=1-0.90⇒α=0.10⇒α/2=0.05

The margin of error, E, for a 100(1-α)% confidence interval is given by

E=Zα/2×σn

As a result, for a90% confidence interval, the margin of error is

E=Z0.05σn=1.645×129∵Z0.05=1.645=6.5794

04

Part (b) Step 1: Calculation

Because the confidence interval is given by (x¯-E,x¯+E), we need to know the sample mean x¯ to get the confidence interval.

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Most popular questions from this chapter

Poverty and Dietary Calcium. Refer to Exercise 8.70.

a. Find a 90%confidence interval for μ.

b. Why is the confidence interval you found in part (a) shorter than the one in Exercise 8.70?

c. Draw a graph similar to that shown in Fig8.6 on page 326 to display both confidence intervals.

d. Which confidence interval yields a more accurate estimate of μ? Explain your answer.

Forearm Length. In 1903, K. Pearson and A. Lee published the paper "On the Laws of Inheritance in Man. I. Inheritance of Physical Characters" (Biometrika, Vol. 2, Pp. 357-462). The article examined and presented data on forearm length, in inches, for a sample of 140 men, which we have provided on the Weiss Stats site. Use the technology of your choice to do the following.

a. Obtain a normal probability plot, boxplot, and histogram of the data.

b. Is it reasonable to apply the t--interval procedure to the data? Explain your answer.

c. If you answered "yes" to part (b), find a 95%confidence interval for men's average forearm length Interpret your result.

Formula 8.2on page 327provides a method for computing the sample size required to obtain a confidence interval with a specified confidence level and margin of error. The number resulting from the formula should be rounded up to the nearest whole number.

a. Why do we want a whole number?

b. Why do we round up instead of down?

When estimating an unknown parameter, what does the margin of error indicate?

Table IV in Appendix A contains degrees of freedom from I to 75 consecutively but then contains only selected degrees of freedom.

a. Why couldn't we provide entries for all possible degrees of freedom?

b. Why did we construct the table so that consecutive entries appear for smaller degrees of freedom but that only selected entries occur for larger degrees of freedom?

c. If you had only Table IV, what value would you use for t0 os with df =87 with df=125? with df=650? with df=3000 ? Explain your answers.
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