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Chapter 6: 9E (page 339)

Question: Will a large-sample confidence interval be valid if the population from which the sample is taken is not normally distributed? Explain.

Short Answer

Expert verified

The confidence interval will be accurate regardless of the method of the population distribution as long as the sample size is large enough to satisfy the Central Limit Theorem.

Step by step solution

01

Confidence interval

A confidence interval shows the likelihood that a variable will fall among two values close to the mean. The confidence level measures the level of uncertainty and certainty in a sampling process.

02

Explanation

Yes. The confidence interval will be accurate regardless of the form of the population distribution as long as the sample is large enough to satisfy the Central Limit Theorem. When the sample size is 30 or greater, they consider the sample to be big, as the sampling distribution will be normal according to the Central Limit Theorem even if the samples do not come from a Normally Distributed one. A bigger sample size and reduced variability result in a narrower confidence range with a narrower error margin

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Most popular questions from this chapter

Study of aircraft bird-strikes. As worldwide air traffic volume has grown over the years, the problem of airplanes striking birds and other flying wildlife has increased dramatically. The International Journal for Traffic and Transport Engineering (Vol. 3, 2013) reported on a study of aircraft bird strikes at Aminu Kano International Airport in Nigeria. During the survey period, a sample of 44 aircraft bird strikes were analyzed. The researchers found that 36 of the 44 bird strikes at the airport occurred above 100 feet. Suppose an airport air traffic controller estimates that less than 70% of aircraft bird strikes occur above 100 feet. Comment on the accuracy of this estimate. Use a 95% confidence interval to support your inference.

Salmonella poisoning from eating an ice cream bar(cont’d). Refer to Exercise 6.132. Suppose it is now 1 yearafter the outbreak of food poisoning was traced to icecream bars. The manufacturer wishes to estimate the proportionwho still will not purchase bars to within .02 usinga 95% confidence interval. How many consumers should be sampled?

Unethical corporate conduct. How complicit are entrylevel accountants in carrying out an unethical request from their superiors? This was the question of interest in a study published in the journal Behavioral Research in Accounting (July 2015). A sample of 86 accounting graduate students participated in the study. After asking the subjects to perform what is clearly an unethical task (e.g., to bribe a customer), the researchers measured each subject’s intention to comply with the unethical request score. Scores ranged from -1.5 (intention to resist the unethical request) to 2.5 (intention to comply with the unethical request). Summary statistics on the 86 scores follow: x¯=2.42,s=2.84.

a. Estimate μ, the mean intention to comply score for the population of all entry-level accountants, using a 90% confidence interval.

b. Give a practical interpretation of the interval, part a.

c. Refer to part a. What proportion of all similarly constructed confidence intervals (in repeated sampling) will contain the true value of μ?

d. Compute the interval, x¯±2s. How does the interpretation of this interval differ from that of the confidence interval, part a?

Use Table III, Appendix D to determine thet0 values foreach of the following probability statements and their respectivedegrees of freedom (df ).

a.Pt⩽t0=.25withdf=15

b.Pt⩾t0=.1withdf=8

c.P-t0⩽t⩽t0=.01withdf=19

d.P-t0⩽t⩽t0=.05withdf=24

Preventing the production of defective items. It costs more toproduce defective items—because they must be scrappedor reworked—than it does to produce non-defective items.This simple fact suggests that manufacturers shouldensurethe quality of their products by perfecting theirproduction processes rather than through inspection of finishedproducts (Out of the Crisis,Deming, 1986). In orderto better understand a particular metal-stamping process, the manufacturer wishes to estimate the mean length of itemsproduced by the process during the past 24 hours.

a. How many parts should be sampled in order to estimatethe population means to within .1 millimetre (mm)with 90% confidence? Previous studies of this machinehave indicated that the standard deviation of lengthsproduced by the stamping operation is about 2 mm.

b. Time permits the use of a sample size no larger than100. If a 90% confidence interval for is constructedusing n= 100, will it be wider or narrower than wouldhave been obtained using the sample size determined in

part a? Explain.

c. If management requires that μbe estimated to within.1 mm and that a sample size of no more than 100 beused, what is (approximately) the maximum confidencelevel that could be attained for a confidence interval

Does that meet management's specifications?
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