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Chapter 8: Q 8.43 (page 330)

Discuss the relationship between the margin of error and the standard error of the mean.

Short Answer

Expert verified

The margin of error and the standard error of the mean are directly proportional to each other.

Step by step solution

01

Given Information

Margin of error is represented by E.

Standard error of sample mean is represented by蟽n.

02

Explanation

Mathematically, the relationship between the two is represented by

E=z伪/2脳蟽n

The above relation is true for 100(1-伪)%Clof population mean 渭.

Hence, margin of error is product of za/2and standard error of sample mean.

Therefore, margin of error is directly proportional to standard error of the mean.

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Most popular questions from this chapter

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).

Assume that the population standard deviation is known and decide weather use of the z-interval procedure to obtain a confidence interval for the population mean is reasonable. Explain your answers.

The sample data contain no outliers, the variable under consideration is roughly normally distributed, and the sample size is 20.

Toxic Mushrooms? Refer to Exercise 8.71

a. Determine and interpret a 99% lower confidence bound for the mean cadmium level of all Boletus Pinicola mushrooms.

b. Compare your one-sided confidence interval in part (a) to the (two-sided) confidence interval found in Exercise 8.71

For a t-curve with df=21, find each f-value, and illustrate your results graphically.

a. The t-value having an area 0.10to its right

b. t0 a1

c. The t-value has an area 0.025to its left (Hint: A t-curve is symmetric at about 0.)

d. The two t-values that divide the area under the curve into a middle 0.90area and two outside areas of 0.05

Fuel Expenditures. In estimating the mean monthly fuel expenditure, 渭, per household vehicle, the Energy Information Ad- ministration takes a sample of size 6841. Assuming that 蟽=$20.65. determine the margin of error in estimating 渭 at the 95% level of confidence.
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