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Chapter 8: Q. 54 (page 480)

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)?

Short Answer

Expert verified

Area in both tails is 伪=0.05.

Step by step solution

01

Given Information

The data in the Table are the result of a random survey of 39national flags (with replacement between picks) from various countries.

xFreq.11273184756

02

Explanation

Mean is nothing but the average of the given set of values. A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

We construct a 100%(1鈭�伪)=95%Confidence Interval for the true mean number of colors on national flags.

So, area in both tails is

伪=1鈭�0.95=0.05.

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Most popular questions from this chapter

If the Census did another survey, kept the error bound the same, and surveyed only 50 people instead of 200, what would happen to the level of confidence? Why?

Define the random variable X in words.

In six packages of 鈥淭he Flintstones庐 Real Fruit Snacks鈥� there were five Bam-Bam snack pieces. The total number of snack pieces in the six bags was 68.We wish to calculate a 96%confidence interval for the population proportion of Bam-Bam snack pieces.

a. Define the random variables XandP鈥�in words.

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

c. Calculatep鈥�.

d. Construct a 96%confidence interval for the population proportion of Bam-Bam snack pieces per bag.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

e. Do you think that six packages of fruit snacks yield enough data to give accurate results? Why or why not?

A poll of 1,200 voters asked what the most significant issue was in the upcoming election. Sixty-five percent answered the economy. We are interested in the population proportion of voters who feel the economy is the most important.

Define the random variable P鈥� in words.

A sample of 16small bags of the same brand of candies was selected. Assume that the population distribution of bag

weights is normal. The weight of each bag was then recorded. The mean weight was two ounces with a standard deviation

of 0.12ounces. The population standard deviation is known to be0.1 ounce.

a.i.x虅=________ii.蟽=________iii.sx=________

b. In words, define the random variableX.

c. In words, define the random variableX虅.

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

e. Construct a 90%confidence interval for the population mean weight of the candies.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

f. Construct a 98%confidence interval for the population mean weight of the candies.

i. State the confidence interval.

ii. Sketch the graph.

iii. Calculate the error bound.

g. In complete sentences, explain why the confidence interval in partf is larger than the confidence interval in part e.

h. In complete sentences, give an interpretation of what the interval in part fmeans.
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