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Chapter 6: Q 6E (page 339)

Explain what is meant by the statement, 鈥淲e are 95% confident that an interval estimate contains 渭.鈥�

Short Answer

Expert verified

In economics, a confidence interval is an approximation of an interval that might include a population parameter. A set of numbers that is expected to encompass a population figure with a reasonable level of certainty.

Step by step solution

01

Step-by-Step Solution Step 1: Explanation

The statement expresses trust in the estimating method instead of on the specific interval determined from the data sample. It states that if this application is repeated numerous times using the identical approach, 95% of the resultant intervals will include 渭.

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Most popular questions from this chapter

Shopping on Black Friday. The day after Thanksgiving鈥� called Black Friday鈥攊s one of the largest shopping days in the United States. Winthrop University researchers conducted interviews with a sample of 38 women shopping on Black Friday to gauge their shopping habits and reported the results in the International Journal of Retail and Distribution Management (Vol. 39, 2011). One question was, 鈥淗ow many hours do you usually spend shopping on Black Friday?鈥� Data for the 38 shoppers are listed in the accompanying table.

a. Describe the population of interest to the researchers.

b. What is the quantitative variable of interest to the researchers?

c. Use the information in the table to estimate the population mean number of hours spent shopping on Black Friday with a 95% confidence interval.

d. Give a practical interpretation of the interval.

e. A retail store advertises that the true mean number of hours spent shopping on Black Friday is 5.5 hours. Can the store be sued for false advertising? Explain.

Calculate the percentage of the population sampled and

the finite population correction factor for each of the following

situations.

a. n= 1,000, N= 2,500

b. n= 1,000, N= 5,000

c. n= 1,000, N= 10,000

d. n= 1,000, N= 100,000

Preventing the production of defective items. It costs more toproduce defective items鈥攂ecause they must be scrappedor reworked鈥攖han 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 渭be 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?

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鈥檚 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炉=2.42,s=2.84.

a. Estimate 渭, 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 渭?

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

Improving the productivity of chickens. Farmers have discovered that the more domestic chickens peck at objects placed in their environment, the healthier and more productive the chickens seem to be. White string has been found to be a particularly attractive pecking stimulus. In one experiment, 72 chickens were exposed to a string stimulus. Instead of white string, blue-colored string was used. The number of pecks each chicken took at the blue string over a specified time interval was recorded. Summary statistics for the 72 chickens were x = 1.13 pecks, s = 2.21 pecks (Applied Animal Behavior Science, October 2000).

a. Estimate population mean number of pecks made by chickens pecking at blue string using a 99% confidence interval. Interpret the result.

b. Previous research has shown that = 7.5 pecks if chickens are exposed to white string. Based on the results, part a, is there evidence that chickens are more apt to peck at white string than blue string? Explain.
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