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Chapter 8: Q. 19 (page 483)

Explain briefly why each of the three conditions—Random, Normal, and Independent—is important when constructing a confidence interval.

Short Answer

Expert verified

Random: It is necessary if we want to generalize the conclusions to the entire population.

Normal: A necessary condition for the construction of the confidence interval.

Independent: Required for the computation of the standard deviation.

Step by step solution

01

Concept Introduction

The probability that a population parameter will fall between a set of values for a particular proportion of the time is referred to as a confidence interval.

02

Explanation

Random: This is required if we wish to apply the findings to the entire population.

Normal: This is a crucial requirement for constructing the confidence interval; if the distribution is not normal, a different approach must be used, as this method may produce inaccurate findings.

Because dependent data might lead to erroneous conclusions, independent data is required for standard deviation computation.

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Most popular questions from this chapter

Watching TV (6.1, 7.3) Choose a young person (aged 19to 25) at random and ask, “In the past seven days, how many days did you watch television?” Call the response Xfor short. Here is the probability distribution for X.

(a) What is the probability that X=7? Justify your answer.

(b) Calculate the mean of the random variable X. Interpret this value in context.

(c) Suppose that you asked 100randomly sele

cted young people (aged 19to 25) to respond to the question and found that the mean xof their responses was 4.96. Would this result surprise you? Justify your answer.

You want to compute a 90%confidence interval for the mean of a population with unknown population standard deviation. The sample size is 30. The value of role="math" localid="1649226392559" tyou would use for this interval is

(a)1.645(b).1.699(c)1.697

(d) 1.96(e) 2.045

60. Travel time to work A study of commuting times reports the travel times to work of a random sample of 20employed adults in New York State. The mean is x¯=31.25 minutes, and the standard deviation is sx=21.88minutes. What is the standard error of the mean? Interpret this value in context.

Abstain from drinking In a Harvard School of Public Health survey, 2105 of 10,904 randomly selected U.S. college students were classified as abstainers (nondrinkers).

(a) Construct and interpret a 99% confidence interval forp. Follow the four-step process.

(b) A newspaper article claims that 25% of U.S. college students are nondrinkers. Use your result from (a) to comment on this claim.

Use Table B to find the critical value t* that you would use for a confidence interval for a population mean M in each of the following situations. If possible, check your answer with technology.

(a) A 98% confidence interval based on n=22observations.

(b) A 90%confidence interval from an SRS of 10observations.

(c) A 95% confidence interval from a sample of size7.
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