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Chapter 8: Q. 19 (page 483)

Explain briefly why each of the three conditions鈥擱andom, Normal, and Independent鈥攊s 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

A quality control inspector will measure the salt content (in milligrams) in a random sample of bags of potato chips from an hour of production. which of the following would result in the smallest margin of error in estimating the mean salt content M?

(a) 90% confidence; n=25.

(b) 90% confidence; n=50.

(c) 95% confidence; n=25.

(d) 95%confidence; n=50.

(e) n=100 at any confidence level.

Equality for women? Have efforts to promote equality for women gone far enough in the United States? A poll on this issue by the cable network MSNBC contacted 1019adults. A newspaper article about the poll said, 鈥淩esults have a margin of sampling error of plus or minus 3 percentage points.鈥�15

(a) The news article said that 65% of men, but only 43% of women, think that efforts to promote equality have gone far enough. Explain why we do not have enough information to give con铿乨ence intervals for men and women separately.

(b) Would a 95% con铿乨ence interval for women alone have a margin of error less than 0.03, about equal to 0.03, or greater than 0.03? Why? (You see that the news article鈥檚 statement about the margin of error for poll results is a bit misleading.)

You have measured the systolic blood pressure of an SRS of 25company employees. A 95%confidence interval for the mean systolic blood pressure for the employees of this company is (122,138). Which of the following statements gives a valid interpretation of this interval?

(a) 95%of the sample employees have systolic blood pressure between 122and138.

(b) 95%of the population of employees have systolic blood pressure between 122and138.

(c) If the procedure were repeated many times, 95%of the resulting confidence intervals would contain the population mean systolic blood pressure.

(d) The probability that the population mean blood pressure is between 122and138is 0.95.

(e) If the procedure were repeated many times, 95%of the sample means would be between122and138.

A 90% confidence interval for the mean M of a population is computed from a random sample and is found to be 9 卤3. Which of the following could be the 95% confidence interval based on the same data?

(a) 9 卤1.96 (b) 9 卤2 (c) 9 卤3 (d) 9 卤4

(e) Without knowing the sample size, any of the above answers could be the 95% confidence interval.

How common is SAT coaching? A random sample of students who took the SAT college entrance examination twice found that 427of the respondents had paid for coaching courses and that the remaining 2733 had not. 1+ Construct and interpret a 99% confidence interval for the proportion of coaching among students who retake the SAT. Follow the four-step process.
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