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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, 渭You know that 蟽=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炉-E,x炉+E)

Step by step solution

01

Part (a) Step 1: Given information

Population s.d.蟽=12

Sample size n=9

02

Part (a) Step 2: Concept

The formula used:E=Z伪/2脳蟽n

03

Part (a) Step 3: Calculation

Population s.d.蟽=12

Sample size n=9

Confidence level =90%=100脳0.90%

鈭�1-伪=0.90鈬�伪=1-0.90鈬�伪=0.10鈬�伪/2=0.05

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

E=Z伪/2脳蟽n

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

E=Z0.05蟽n=1.645脳129鈭�Z0.05=1.645=6.5794

04

Part (b) Step 1: Calculation

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

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Most popular questions from this chapter

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.

The margin of error can be determined if you know only the confidence level, population standard deviation, and sample size.

M\&Ms. In the article "Sweetening Statistics-What M\&M's Can Teach Us" (Minitab Inc., August 2008), M. Paret and E. Martz discussed several statistical analyses that they performed on bags of M\&Ms. The authors took a random sample of 30 small bags of peanut M\&Ms and obtained the following weights, in grams (g).

a. Determine a 95%lower confidence bound for the mean weight of all small bags of peanut M\&Ms. (Note: The sample mean and sample standard deviation of the data are 52.040gand 2.807grespectively.)

b. Interpret your result in pant (a).

c. According to the package, each small bag of peanut M\&Ms should weigh 49.3gComment on this specification in view of your answer to part (b) It provides equal confidence with a greater lower limit.

Part (c) Because the weight of 49.3g is below the 95% lower confidence bound.

State True or False. Give Reasons for your answers..

The confidence interval can be obtained if you know only the margin of error.

Explain why the margin of error determines the accuracy with which a sample mean estimates a population mean.
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