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Chapter 8: Q.11 (page 525)

The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favour the proposal. Of these, 89 say 鈥淵es.鈥�

(a) Construct and interpret a 99% confidence interval for the proportion of all visitors to Yellowstone who favours the restrictions.

(b) Based on your work in part (a), can the U.S. Forest Service conclude that more than half of visitors to Yellow-stone National Park favour the proposal? Justify your answer.

Short Answer

Expert verified

a. the confidence interval is(0.49,0.70)

b. No

Step by step solution

01

introduction

Given, the service asks a random sample n =150

people who say yes x = 89

Using,

p^鈭�za2脳p^脳(1鈭�p^)n<p<p^鈭�za2脳p^脳(1鈭�p^)n

99%confidence interval for the proportion of all visitors to Yellowstone who favours the restrictions is(0.49,0.70)

02

explanation

From the above part, it is realized that the population extent is somewhere in the range of0.49and0.70. No, the U.S. Forest Service cant conclude that more than half of visitors to Yellow-stone National Park favour the proposal since the interval has the range0.49. Accordingly, it can't be inferred that the greater part of the guests are supportive of the proposition.

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Most popular questions from this chapter

Teens" online profiles Describe a possible source of error that is not included in the margin of error for the 95% confidence interval in Exercise 36

A milk processor monitors the number of bacteria per millilitre in raw milk received at the factory. A random sample of 10 one-millilitre specimens of milk supplied by one producer gives the following data:

5370 4890 5100 4500 5260 5150 4900 4760 4700 4870

Construct and interpret a 90% confidence interval for the population mean 渭.

One reason for using a tdistribution instead of the standard Normal curve to find critical values when calculating a level C confidence interval for a population mean is that

(a) zcan be used only for large samples.

(b) zrequires that you know the population standard deviation 蟽.

(c) zrequires that you can regard your data as an SRS from the population.

(d) the standard Normal table doesn't include confidence levels at the bottom.

(e) a zcritical value will lead to a wider interval than a tcritical value.

2K10 begins In January 2010, a Gallup Poll asked a random sample of adults, "In general, are you satisfied or dissatisfied with the way things are going in the United States at this time?" In all, 256said that they were sitisfied and the remaining 769said they were not. Construct and interpret a90%confidence interval for the proportion of adults who are satisfied with how things are going. Follow the four-step process.

Do you go to church? The Gallup Poll plans to ask a random sample of adults whether they attended a religious service in the last 7days. How large a sample would be required to obtain a margin of error of 0.01ina99%confidence interval for the population proportion who would say that they attended a religious service? Show your work.

- Construct and interpret a confidence interval for a population proportion.

- Explain how practical issues like nonresponse, under coverage, and response bias can affect the interpretation of a confidence interval.
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