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Chapter 8: Q.8.6 (page 455)

Suppose we know that a confidence interval is (42.12,47.88). Find the error bound and the sample mean.

Short Answer

Expert verified

The error bound and the sample mean are:

x炉=45EMB=2.88.

Step by step solution

01

Given Information

The term "error bound,'' is an upper bound on the size of the error

02

Explanation

If x-is the sample mean of a random sample of size n from a normal population with known variance, a Cl (confidence interval) on 渭is provided by

x炉鈭�EBM鈮�渭鈮�x炉+EBM

Where EBM is the error bound for a population mean.

We know that Cl is (42.12,47.88), but we do not know the sample mean and the error bound for the mean. Therefore sample mean is

x炉=42.12+47.882=45

and error bound is

EBM=47.88鈭�42.122=2.88

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Most popular questions from this chapter

Using the same mean, standard deviation, and sample size, how would the error bound change if the confidence level were reduced to 90%? Why?

Fill in the blanks on the graph with the areas, upper and lower limits of the confidence interval, and the sample mean.

If the Census wants to increase its level of confidence and keep the error bound the same by taking another survey, what changes should it make?

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its mean number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is 4.1 seats.

a. i. x=__________

ii. sx=__________

iii. n=__________

iv. n-1=__________

b. Define the random variables Xand Xin words.

c. Which distribution should you use for this problem? Explain your choice.

d. Construct a 92% confidence interval for the population mean number of unoccupied seats per flight.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

Fill in the blanks on the graph with the areas, upper and lower limits of the confidence interval, and the sample

proportion.
See all solutions

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