a. Explanation Calculation: It is given that the sample size n is 240. The percentage of people smoking is 15%. Sampling distribution of p ¯ : The probability distribution of 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 as follows: For finite population, σ p ¯ = N − n N − 1 p ( 1 − p ) n . Here, N represents population size, n represents sample size, and p represents population proportion. 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 as follows: E ( p ¯ ) = p = 0 b. To determine Find the probability that the sample proportion will be within ± .04 of the population proportion. c. To determine Find the probability that the sample proportion will be within ± .02 of the population proportion.

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

6th Edition

ISBN: 9780357191484

Author: David R. Anderson; Dennis J. Sweeney; Thomas A. Williams

Publisher: Cengage Learning US

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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, Problem 50SE

To determine

Show the sampling distribution of p¯.

To determine

Find the probability that the sample proportion will be within ±.04 of the population proportion.

To determine

Find the probability that the sample proportion will be within ±.02 of the population proportion.

Expert Solution & Answer

Chapter 7 Solutions

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

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...

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Show the sampling distribution of p ¯ .

Solution Summary: The author illustrates the sampling distribution of stackrel p. The sample size n is 240 and the percentage of people smoking is 15%.

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Show the sampling distribution of p¯.

Find the probability that the sample proportion will be within ±.04 of the population proportion.

Find the probability that the sample proportion will be within ±.02 of the population proportion.

Chapter 7 Solutions