a. Explanation Calculation: The given information is that the sample of 400 consumers is drawn from the population. Consider the population proportion as 0.76. Sampling distribution of p ¯ : The probability distribution all possible values of the sample proportion p ¯ is termed as the sampling distribution of p ¯ . The expected value of p ¯ is, E ( p ¯ ) = p . The standard deviation of p ¯ is For finite population, σ p ¯ = N − n N − 1 p ( 1 − p ) n For infinite population, σ p ¯ = p ( 1 − p ) n When n p ≥ 5 and n ( 1 − p ) ≥ 5 then the sampling distribution of p ¯ is approximated by a normal distribution. The expected value is, E ( p ¯ ) = p = 0.76 Thus, the expected value of p ¯ is 0.76. The standard deviation of p ¯ is σ p ¯ = p ( 1 − p ) n Substitute p as 0 b. To determine Find the probability that the sample proportion will be within ± .03 of the population proportion. c. To determine Find the probability that the sample proportion will be within ± .03 of the population proportion for sample size 750.

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

6th Edition

ISBN: 9781337115186

Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran

Publisher: Cengage Learning

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Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Chapter 7.6, Problem 36E

To determine

Show the sampling distribution of p¯ where p¯ is the proportion of the sampled consumers who read the ingredients listed on a product’s label.

To determine

Find the probability that the sample proportion will be within ±.03 of the population proportion.

To determine

Find the probability that the sample proportion will be within ±.03 of the population proportion for sample size 750.

Expert Solution & Answer

Chapter 7 Solutions

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Ch. 7.2 - Consider a finite population with five elements...Ch. 7.2 - Assume a finite population has 10 elements. Number...Ch. 7.2 - The 2012 American League consists of 14 baseball...Ch. 7.2 - The U.S. Golf Association has instituted a ban on...Ch. 7.2 - In this section we used a two-step procedure to...Ch. 7.2 - 10. Indicate which of the following situations...Ch. 7.3 - 11. The following data are from a simple random...Ch. 7.3 - Prob. 8E Ch. 7.3 - Prob. 9E Ch. 7.3 - 14. Morningstar publishes ratings data on 1208...

Ch. 7.3 - 15. The National Football League (NFL) polls fans...Ch. 7.3 - AARP Survey. In a sample of 426 U.S. adults age 50...Ch. 7.3 - 17. One of the questions in the Pew Internet &...Ch. 7.3 - In this section we showed how a simple random...Ch. 7.5 - 19. A population has a mean of 200 and a standard...Ch. 7.5 - Prob. 16E Ch. 7.5 - 21. Suppose a random sample of size 50 is selected...Ch. 7.5 - Refer to the EAI sampling problem. Suppose a...Ch. 7.5 - In the EAI sampling problem (see Figure 7.8), we...Ch. 7.5 - 24. Barron’s reported that the average number of...Ch. 7.5 - The average full-sized front-loading Energy Star...Ch. 7.5 - Federal Income Tax Returns. The Wall Street...Ch. 7.5 - 27. The Economic Policy Institute periodically...Ch. 7.5 - State Rainfalls. The state of California has a...Ch. 7.5 - The mean preparation fee H&R Block charged retail...Ch. 7.5 - 30. To estimate the mean age for a population of...Ch. 7.6 - 31. A sample of size 100 is selected from a...Ch. 7.6 - 32. A population proportion is .40. A sample of...Ch. 7.6 - Prob. 29E Ch. 7.6 - 34. The population proportion is .30. What is the...Ch. 7.6 - Prob. 31E Ch. 7.6 - 36. The Wall Street Journal reported that the age...Ch. 7.6 - Seventy two percent of American adults have read a...Ch. 7.6 - Unnecessary Medical Care. According to Reader’s...Ch. 7.6 - Thirty-six percent of all Americans drink bottled...Ch. 7.6 - Prob. 36E Ch. 7.6 - 41. The Food Marketing Institute shows that 17% of...Ch. 7.8 - Martina Levitt, director of marketing for the...Ch. 7.8 - Consider the Spontanversation sampling problem for...Ch. 7.8 - The Wall Street Journal reported that 37% of all...Ch. 7.8 - The vice president of sales for Blasterman...Ch. 7 - Shadow Stocks. Jack Lawler, a financial analyst,...Ch. 7 - 43. The latest available data showed health...Ch. 7 - 44. Foot Locker uses sales per square foot as a...Ch. 7 - 45. Allegiant Airlines charges a mean base fare of...Ch. 7 - 46. After deducting grants based on need, the...Ch. 7 - Prob. 47SE Ch. 7 - Prob. 48SE Ch. 7 - Production Quality Control. A production process...Ch. 7 - Prob. 50SE Ch. 7 - Prob. 51SE Ch. 7 - Prob. 52SE Ch. 7 - Prob. 53SE Ch. 7 - 54. Lori Jeffrey is a successful sales...Ch. 7 - Managerial Report Prepare a managerial report that...

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Show the sampling distribution of p ¯ where p ¯ is the proportion of the sampled consumers who read the ingredients listed on a product’s label.

Concept explainers

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Show the sampling distribution of p¯ where p¯ is the proportion of the sampled consumers who read the ingredients listed on a product’s label.

Find the probability that the sample proportion will be within ±.03 of the population proportion.

Find the probability that the sample proportion will be within ±.03 of the population proportion for sample size 750.

Chapter 7 Solutions