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Consider the following population: (6, 7, 8, 9). For this population the mean is Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account). 8,6 8,7 8,9 9,6 9,7 9,8 (a) Calculate the sample mean for each of the 12 possible samples. Sample Sample Mean 6,9 O 7,6 7,9 8,6 8,7 8,9 9,7 (b) Use the sample means to construct the sampling distribution of x. Display the sampling distribution as a density histogram. Density 0.8 , 0.6 Density 0.4 02 0.0 6+7+8+9 4 0.6 -7.5 0.4 0.2 0.0 6.5 7 7.5 Sample Mean 8.5 6 6.5 7 7.5 8 Sample Mean 9.5 Density Ⓡ 0.8 Density 0.6 0.4 0.2 0.0 0.6 0.4 0.2 6.5 7 0.0 7.5 Sample Mean 6 6.5 7 7.5 8 8.5 9 9.5 O Sample Mean Density 0.8 Density 0.6 0.4 0.2 0.0 (c) Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of part (a), construct the sampling distribution of x. (Hint: There are 16 different possible samples in this cas 0.8 0.8 0.8 08 0.6 0.4 0.2 6.5 0.0 7 7.5 Sample Mean 6 6.5 7 8 8.5 7.5 8 8.5 9 9.5 Sample Mean Density DO 0.8 Density 0.6 0.4 0.2 0.0 0.6 0.4 0.2 6.5 0.0 7 6 6.5 7.5 Sample Mean 8 8.5 7 7.5 8 8.5 9 9.5 Sample Mean G

Consider the following population: (6, 7, 8, 9). For this population the mean is Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account). 8,6 8,7 8,9 9,6 9,7 9,8 (a) Calculate the sample mean for each of the 12 possible samples. Sample Sample Mean 6,9 O 7,6 7,9 8,6 8,7 8,9 9,7 (b) Use the sample means to construct the sampling distribution of x. Display the sampling distribution as a density histogram. Density 0.8 , 0.6 Density 0.4 02 0.0 6+7+8+9 4 0.6 -7.5 0.4 0.2 0.0 6.5 7 7.5 Sample Mean 8.5 6 6.5 7 7.5 8 Sample Mean 9.5 Density Ⓡ 0.8 Density 0.6 0.4 0.2 0.0 0.6 0.4 0.2 6.5 7 0.0 7.5 Sample Mean 6 6.5 7 7.5 8 8.5 9 9.5 O Sample Mean Density 0.8 Density 0.6 0.4 0.2 0.0 (c) Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of part (a), construct the sampling distribution of x. (Hint: There are 16 different possible samples in this cas 0.8 0.8 0.8 08 0.6 0.4 0.2 6.5 0.0 7 7.5 Sample Mean 6 6.5 7 8 8.5 7.5 8 8.5 9 9.5 Sample Mean Density DO 0.8 Density 0.6 0.4 0.2 0.0 0.6 0.4 0.2 6.5 0.0 7 6 6.5 7.5 Sample Mean 8 8.5 7 7.5 8 8.5 9 9.5 Sample Mean G

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Consider the following population: (6, 7, 8, 9). For this population the mean is O P- Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account). 6,7 6,8 6,9 7,6 7,8 7,9 8,6 8,7 8,9 9,6 9,7 9,8 (a) Calculate the sample mean for each of the 12 possible samples. Sample Sample Mean 7,9 9,6 9,8 Density (b) Use the sample means to construct the sampling distribution of x. Display the sampling distribution as a density histogram. Density 0.8 0.6 0.4 0.0 0.6 6+7+8+9 4 0.4 0.2 - 7.5 0.0 6.5 7 7.5 8 8.5 Sample Mean 6 6.5 7 7.5 8 8.5 Sample Mean Density 9.5 Their means are equal. They are both symmetrical. Their means are different. 0.8 Density 0.6 0.4 0.0 0.6 0.4 0.2 6.5 7 0.0 7.5 8 Sample Mean 6 6.5 7 7.5 Sample Mean 8 8.5 8.5 9.5 Density (c) Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of part (a), construct the sampling distribution of x. (Hint: There are 16 different possible samples in this case.) 0.8 0.8 08 0.8 O 0.8 Density 0.6 0.4 0.2 0.0 ast 0.4 02 0.0 (d) In what ways are the two sampling distributions of parts (b) and (c) similar? In what ways are they different? (Select all that apply.) They both cover the same range. One distribution covers a larger range. One distribution is not symmetrical. 6.5 7 6 6.5 7.5 8 Sample Mean 7 7.5 8 8.5 8.5 Sample Mean O 9.5 Density 0.8 Density 0.6 0.4 0.2 0.0 0.6 0.4 02 6.5 7 0.0 7.5 8 8.5 Sample Mean 6 6.5 7 7.5 8 8.5 Sample Mean 9.5
Transcribed Image Text:Consider the following population: (6, 7, 8, 9). For this population the mean is O P- Suppose that a random sample of size 2 is to be selected without replacement from this population. There are 12 possible samples (provided that the order in which observations are selected is taken into account). 6,7 6,8 6,9 7,6 7,8 7,9 8,6 8,7 8,9 9,6 9,7 9,8 (a) Calculate the sample mean for each of the 12 possible samples. Sample Sample Mean 7,9 9,6 9,8 Density (b) Use the sample means to construct the sampling distribution of x. Display the sampling distribution as a density histogram. Density 0.8 0.6 0.4 0.0 0.6 6+7+8+9 4 0.4 0.2 - 7.5 0.0 6.5 7 7.5 8 8.5 Sample Mean 6 6.5 7 7.5 8 8.5 Sample Mean Density 9.5 Their means are equal. They are both symmetrical. Their means are different. 0.8 Density 0.6 0.4 0.0 0.6 0.4 0.2 6.5 7 0.0 7.5 8 Sample Mean 6 6.5 7 7.5 Sample Mean 8 8.5 8.5 9.5 Density (c) Suppose that a random sample of size 2 is to be selected, but this time sampling will be done with replacement. Using a method similar to that of part (a), construct the sampling distribution of x. (Hint: There are 16 different possible samples in this case.) 0.8 0.8 08 0.8 O 0.8 Density 0.6 0.4 0.2 0.0 ast 0.4 02 0.0 (d) In what ways are the two sampling distributions of parts (b) and (c) similar? In what ways are they different? (Select all that apply.) They both cover the same range. One distribution covers a larger range. One distribution is not symmetrical. 6.5 7 6 6.5 7.5 8 Sample Mean 7 7.5 8 8.5 8.5 Sample Mean O 9.5 Density 0.8 Density 0.6 0.4 0.2 0.0 0.6 0.4 02 6.5 7 0.0 7.5 8 8.5 Sample Mean 6 6.5 7 7.5 8 8.5 Sample Mean 9.5
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