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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 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.

Short Answer

Expert verified

confidence interval based on the same data is (d)9卤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卤margin of error

02

explanation

confidence interval = points estimate卤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卤4.

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Most popular questions from this chapter

Hallux abducto valgus (call it HAV) is a deformation of the big toe that is fairly uncommon in youth and often requires surgery. Doctors used X-rays to measure the angle (in degrees) of deformity in a random sample of patients under the age of 21who came to a medical center for surgery to correct HAV. The angle is a measure of the seriousness of the deformity. For these 21patients, the mean HAV angle was 24.76degrees and the standard deviation was 6.34degrees. A dot plot of the data revealed no outliers or strong skewness.

(a) Construct and interpret a 90%confidence interval for the mean HAV angle in the population of all such patients.

(b) Researchers omitted one patient with an HAV angle of 50degrees from the analysis due to a measurement issue. What effect would including this outlier have on the confidence interval in (a)? Justify your answer.

98% Confidence find z*for a98%confidence interval using table A or tour calculator. show your method.

A telephone poll of an SRS of 1234 adults found that 62% are generally satisfied with their lives. The announced margin of error for the poll was 3%. Does the margin of

error account for the fact that some adults do not have telephones?

(a) Yes. The margin of error includes all sources of error in the poll.

(b) Yes. Taking an SRS eliminates any possible bias in estimating the population proportion.

(c) Yes. The margin of error includes under coverage but not nonresponse.

(d) No. The margin of error includes nonresponse but is not under coverage.

(e) No. The margin of error only includes sampling variability.

Running red lights A random digit dialing telephone survey of880drivers asked, "Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?" Of the 880respondents, 171admitted that at least one light had been red.15

(a) Construct and interpret a95%confidence interval for the population proportion.

(b) Nonresponse is a practical problem for this survey-only 21.6%of calls that reached a live person were completed. Another practical problem is that people may not give truthful answers. What is the likely direction of the bias: do you think more or fewer than 171of the 880respondents really ran a red light? Why? Are these sources of bias included in the margin of error?

You have an SRS of 23 observations from a Normally distributed population. What critical value would you use to obtain a 98% confidence interval for the mean M of the population if S is unknown?

(a) 2.508

(b) 2.500

(c) 2.326

(d) 2.183

(e) 2.177
See all solutions

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