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Chapter 8: Q 19. (page 508)

Prayer in school Refer to Exercise 5.

a. Explain what would happen to the length of the interval if the confidence level were increased to 99%.

b. How would a 95%confidence interval based on double the sample size compare to the original 95%interval?

c. The news article goes on to say: 鈥淭he theoretical errors do not take into account

additional errors resulting from the various practical difficulties in taking any survey of public opinion.鈥� List some of the 鈥減ractical difficulties鈥� that may cause errors which are not included in the 卤3 percentage point margin of error.

Short Answer

Expert verified

a. The length of interval increases.

b. On basis of double the sample size, confidence interval is narrower than original confidence interval.

c. It is not accountable for errors made during date of sample collection.

Step by step solution

01

Given Information

Confidence levels of95%,99%are given.

02

a. To explain effect on length of interval

If confidence level increases from 95%to99%, confidence that interval is having true parameter of population increases.

It has more possible values of true population parameter.

Hence, length of interval increases.

03

b. To explain how would a 95%confidence interval based on double the sample size compare to the original 95% interval.

Sample size increases when sample size is doubled. Hence, it will have more data about population and more correct estimates would be obtained.

Estimates would be more close to true value.

Hence., confidence interval needs to be narrower.

04

c. To determine that not included in ±3 percent point margin of error.

Margin of error contains possible variations only. It is not responsible for the errors made while collecting sample date.

Possible bias are:

  • Selection will exclude portion of population.
  • Response bias will use procedure showing values different from correct value.
  • Not containing data for everybody will cause no response bias.

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Most popular questions from this chapter

California鈥檚 traffic People love living in California for many reasons, but traffic isn鈥檛 one of them. Based on a random sample of 572employed California adults, a 90%confidence interval for the average travel time to work for all employed California adults is 23minutes to 26 minutes.

a. Interpret the confidence level.

b. Name two things you could do to reduce the margin of error. What drawbacks do these actions have?

c. Describe how non response might lead to bias in this survey. Does the stated margin of error account for this possible bias?

The student body president of a high school claims to know the names of at least 1000of the 1800 students who attend the school. To test this claim, the student government advisor randomly selects 100students and asks the president to identify each by name. The president successfully names only 46of the students.

a. Identify the population and parameter of interest.

b. Check conditions for constructing a confidence interval for the parameter.

c. Construct a 99%confidence interval for p.

d. Interpret the interval in context.

It鈥檚 critical Find the appropriate critical value for constructing a confidence interval in each of the following settings.

a. Estimating a population proportion p at a 94% confidence level based on an SRS of size 125

b. Estimating a population mean 渭 at a 99% confidence level based on an SRS of size 58

Batteries A company that produces AA batteries tests the lifetime of a randomsample of 30 batteries using a special device designed to imitate real-world use. Based onthe testing, the company makes the following statement: 鈥淥ur AA batteries last an average of 430 to 470 minutes, and our confidence in that interval is 95%.鈥�36

a. Determine the point estimate, margin of error, standard error, and sample standard

deviation.

b. A reporter translates the statistical announcement into 鈥減lain English鈥� as follows: 鈥�95% of this company鈥檚 AA batteries last between 430 and 470 minutes.鈥� Comment on this interpretation.

c. Your friend, who has just started studying statistics, claims that there is a 95% probability that the mean lifetime will fall between 430 and 470 minutes. Do you agree? Explain your reasoning.

d. Give a statistically correct interpretation of the confidence level that could be published in a newspaper report.

Most people can roll their tongues, but many can鈥檛. The ability to roll the tongue is

genetically determined. Suppose we are interested in determining what proportion of students can roll their tongues. We test a simple random sample of 400students and find that 317can roll their tongues. The margin of error for a 95%confidence interval for the true proportion of tongue rollers among students is closest to which of the following?

a. 0.0008

b. 0.02

c. 0.03

d. 0.04

e. 0.05
See all solutions

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