The following information gives the number of days absent from work for a popula
ID: 3217448 • Letter: T
Question
The following information gives the number of days absent from work for a population of 40 students in a statistics class.
1 Find the mean and the standard deviation for the population. (Hint: there is a difference between the sample and the population standard deviation.)
2 Samples of size 5 will be drawn from the population. Use the answers in part (a) to calculate the expected value and the standard deviation of the sampling distribution of the sample mean.
3 How many samples of 5 students can be extracted from this population? Choose the samples without replacement. (You just need to give the number, not list all the possible samples.)
Student Number of Days Absent
1 0
2 1
3 1
4 1
5 1
6 2
7 0
8 0
9 1
10 2
11 0
12 0
13 0
14 14
15 0
16 1
17 2
18 2
19 2
20 0
21 0
22 0
23 0
24 0
25 2
26 0
27 0
28 2
29 0
30 0
31 1
32 2
33 1
34 0
35 0
36 1
37 0
38 4
39 10
40 0
Explanation / Answer
1. Population mean = mean of (0,1,1,1,1,2,0,0,1,2,0,0,0,14,0,1,2,2,2,0,0,0,0,0,2,0,0,2,0,0,1,2,1,0,0,1,0,4,10,0)
= sum of all 40 numbers/ 40 = 1.325
Population std deviation = std deviation of (0,1,1,1,1,2,0,0,1,2,0,0,0,14,0,1,2,2,2,0,0,0,0,0,2,0,0,2,0,0,1,2,1,0,0,1,0,4,10,0)
= 2.692701
2. Sample mean = Population mean = 1.325
Sample std deviation = Population std deviation / sqrt(n) where n = 40
= 2.692701 / sqrt(40) = 0.4257534
3. From the population of 40 students, there can be 40/5 = 8 samples without replacement of 5 students can be extracted from this population.
Updated - The population contains 40 students. We need to take sample of 5 students that is each sample contains 5 students. As this is a sample without replacement, each sample must have different students.
So, total number of samples = 40/5 = 8
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