(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 O Density Density 0.6 0.4 0.2 0.0 0.8 0.6 0.4 0.2 0.0 6 6.5 7 7.5 6 6.5 7 8 8.5 9 9.5 Sample Mean 7.5 Sample Mean 8 8.5 9 9.5 O Density Density 0.6 0.4 0.2 0.0 0.8 0.6 0.4 0.2 0.0 6 6.5 7 6 6.5 7 7.5 8 8.5 9 9.5 Sample Mean 8 8.5 9 9.5 7.5 Sample Mean Ⓡ

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(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
O
Density
Density
0.6
0.4
0.2
0.0
0.8
0.6
0.4
0.2
0.0
6
6
6.5
6.5
7 7.5
7
8 8.5 9 9.5
Sample
Mean
7.5
Sample
Mean
8
8.5
9 9.5
GO
Density
Density
0.6
0.4
0.2
0.0
0.8
0.6
0.4
0.2
0.0
6
6
6.5 7 7.5 8 8.5 9 9.5
Sample
Mean
6.5
7
8
7.5
Sample
Mean
8.5 9 9.5
Ⓡ
Transcribed Image Text:(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 O Density Density 0.6 0.4 0.2 0.0 0.8 0.6 0.4 0.2 0.0 6 6 6.5 6.5 7 7.5 7 8 8.5 9 9.5 Sample Mean 7.5 Sample Mean 8 8.5 9 9.5 GO Density Density 0.6 0.4 0.2 0.0 0.8 0.6 0.4 0.2 0.0 6 6 6.5 7 7.5 8 8.5 9 9.5 Sample Mean 6.5 7 8 7.5 Sample Mean 8.5 9 9.5 Ⓡ
Consider the following population: {6, 7, 8, 9). For this population the mean is
6 + 7 + 8 + 9
4
μl =
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
8, 6
6,7
Sample Sample Mean
6,8
6,9
(a) Calculate the sample mean for each of the 12 possible samples.
7,6
= 7.5
7,8
7,9
6,8 6,9 7,6
8,7
8,9
8, 6
9,6
7,8 7,9
9, 79, 8
Transcribed Image Text:Consider the following population: {6, 7, 8, 9). For this population the mean is 6 + 7 + 8 + 9 4 μl = 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 8, 6 6,7 Sample Sample Mean 6,8 6,9 (a) Calculate the sample mean for each of the 12 possible samples. 7,6 = 7.5 7,8 7,9 6,8 6,9 7,6 8,7 8,9 8, 6 9,6 7,8 7,9 9, 79, 8
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