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Chapter 8: Q.7 (page 524)

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

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

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

Short Answer

Expert verified

confidence interval based on the same data is (d)9±4

Step by step solution

01

introduction

we know,

the confidence interval is 95%

For calculating the mean population the confidence interval is

confidence interval = points estimate±margin of error

02

explanation

confidence interval = points estimate±margin of error

The width of the confidence interval is addressed by the safety buffer and the width is straightforwardly connected with the degree of confidence.

Here, in the event that 95%confidence level is utilized rather than 90%, the confidence interval would be more extensive which implies that the margin of error ought to be over 3. Thus, out of the relative multitude of choices, the confidence interval is 9±4.

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Most popular questions from this chapter

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

Critical value What critical value t*from Table B would you use for a 90%confidence interval for the population mean based on an SRS of size 77? If possible, use technology to find a more accurate value of . What advantage does the more accurate df provide?

How heavy a load (pounds) is needed to pull apart pieces of Douglas fir 4inches long and 1.5inches square? A random sample of 20similar pieces of Douglas fir from a large batch was selected for a science class. The Fathom boxplot below shows the class’s data. Explain why it would not be wise to use a one-sample t interval to estimate the population meanμ.

Many television viewers express doubts about the validity of certain commercials. In an attempt to answer their critics, Timex Group USA wishes to estimate the proportion of consumers who believe what is shown in Timex television commercials. Let prepresent the true proportion of consumers who believe what is shown in Timex television commercials. What is the smallest number of consumers that Timex can survey to guarantee a margin of error of 0.05or less at a 99%confidence level?

(a) 550

(b) 600

(c) 650

(d) 700

(c)750

Reporting cheating What proportion of students are willing to report cheating by other students? A student project put this question to an SRS of 172 undergraduates at a large university: “You witness two students cheating on a quiz. Do you go to the professor?” Only 19 answered “Yes.”3
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