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Chapter 8: Q.8.61 (page 481)

The data in Table 8.10 are the result of a random survey of 39 national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X = the number of colors on a national flag.

Construct a 95% confidence interval for the true mean number of colors on national flags.

Using the same x¯ , sx , and n = 39, how would the error bound change if the confidence level were reduced to 90%? Why?

Short Answer

Expert verified

The error bound will be smaller.

Step by step solution

01

Given information

Given in the question that

X=the number of colors on a national flag

02

Solution

Error bound

The Lagrange error bound of a Taylor polynomial shows the worst-case method for the distinction between the assessed value of the procedure as delivered by the Taylor polynomial and the actual value of the function.

Here the confidence level is reduced to 90%

The sample mean, sample size, and sample standard deviation are the same.

So the formula is,

EBM=tn−1α2sn

The error bound decreases if the confidence level decreases because the confidence level decreases the area under the curve to capture the true population mean is less.

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Most popular questions from this chapter

The data in Table are the result of a random survey of 39national flags (with replacement between picks) from various countries. We are interested in finding a confidence interval for the true mean number of colors on a national flag. Let X=the number of colors on a national flag.

XFreq.11273184756

Is σxknown.

Which distribution should you use for this problem?

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

What would happen if 40 heads of lettuce were sampled instead of 20, and the error bound remained the same?

Identify the following:

a. x=_______

b. sx =_______

c. n =_______

d. n – 1 =_______
See all solutions

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