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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

Cybersecurity survey. Refer to the State of Cybersecurity (2015) survey of firms from around the world, Exercise 1.20 (p. 50). Recall that of the 766 firms that responded to the survey, 628 (or 82%) expect to experience a cyberattack (e.g., a Malware, hacking, or phishing attack) during the year. Estimate the probability of an expected cyberattack at a firm during the year with a 90% confidence interval. Explain how 90% is used as a measure of reliability for the interval.

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a. Locate the 90% confidence interval for 蟽2on the printout. Interpret the result. b. Use the sample variance on the printout to calculate the 90% confidence interval for蟽2. Does your result agree with the interval shown on the printout?

c. Locate the 90% confidence interval for on the printout.

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