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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炉 , 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鈭�1伪2sn

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

In one complete sentence, explain what the interval means.

Suppose that a committee is studying whether or not there is waste of time in our judicial system. It is interested in

the mean amount of time individuals waste at the courthouse waiting to be called for jury duty. The committee randomly

surveyed 81people who recently served as jurors. The sample mean wait time was eight hours with a sample standard

deviation of four hours.

a.i.x虅=__________ii.sx=__________iii.n=__________iv.n鈥�1=__________

b. Define the random variables XandX虅in words.

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

d. Construct a 95%confidence interval for the population mean time wasted.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. Explain in a complete sentence what the confidence interval means.

When designing a study to determine this population proportion, what is the minimum number you would need to survey to be 90% confident that the population proportion is estimated to within 0.05 ?

Using the same p鈥� and level of confidence, suppose that n were increased to 100. Would the error bound become larger

or smaller? How do you know?

The data in the 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

Construct a95%confidence interval for the true mean number of colors on national flags.

How much area is in both tails (combined)?
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