Central Limit Theorem Twenty students from a statistics class each collected a random sample of times on how long it tookstudents to get to class from their homes. All the sample sizes were 30. The resulting means are listed. Student Мean Std. Dev. Student Mean Std. Dev. 1 22 3.7 11 27 1.4 31 4.6 12 24 2.2 3 18 2.4 13 14 3.1 27 20 4 1.9 14 29 2.4 5 3.0 15 37 2.8 17 2.8 16 23 2.7 7 26 1.9 17 26 1.8 8 34 4.2 18 21 2.0 9 23 2.6 19 30 2.2 10 29 2.1 20 29 2.8 a. Isthe distribution of the means a sampling distribution? b. Checkthe sampling error for students 3,7, and 14. c. Compare the standard deviation of the sample of the 20 means. Is that equal to the standard deviation from student 3 divided by the square of the sample size? How about for student 7, or 14?

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Central Limit Theorem
Twenty students from a statistics class each collected a random sample of times on
how long it tookstudents to get to class from their homes. All the sample sizes were
30. The resulting means are listed.
Student
Мean
Std. Dev.
Student
Mean
Std. Dev.
1
22
3.7
11
27
1.4
31
4.6
12
24
2.2
3
18
2.4
13
14
3.1
27
20
4
1.9
14
29
2.4
5
3.0
15
37
2.8
17
2.8
16
23
2.7
7
26
1.9
17
26
1.8
8
34
4.2
18
21
2.0
9
23
2.6
19
30
2.2
10
29
2.1
20
29
2.8
a. Isthe distribution of the means a sampling distribution?
b. Checkthe sampling error for students 3,7, and 14.
c. Compare the standard deviation of the sample of the 20 means. Is that equal
to the standard deviation from student 3 divided by the square of the sample
size? How about for student 7, or 14?
Transcribed Image Text:Central Limit Theorem Twenty students from a statistics class each collected a random sample of times on how long it tookstudents to get to class from their homes. All the sample sizes were 30. The resulting means are listed. Student Мean Std. Dev. Student Mean Std. Dev. 1 22 3.7 11 27 1.4 31 4.6 12 24 2.2 3 18 2.4 13 14 3.1 27 20 4 1.9 14 29 2.4 5 3.0 15 37 2.8 17 2.8 16 23 2.7 7 26 1.9 17 26 1.8 8 34 4.2 18 21 2.0 9 23 2.6 19 30 2.2 10 29 2.1 20 29 2.8 a. Isthe distribution of the means a sampling distribution? b. Checkthe sampling error for students 3,7, and 14. c. Compare the standard deviation of the sample of the 20 means. Is that equal to the standard deviation from student 3 divided by the square of the sample size? How about for student 7, or 14?
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