the sports authority sells five different medicine balls with weights (in kilogr
ID: 3171794 • Letter: T
Question
the sports authority sells five different medicine balls with weights (in kilograms) given in the table below
10, 12, 15, 18, 25
a.) find the population mean and the population median.
b.) suppose a random sample of size 3 is selected from this population without replacement. Find the sampling distribution of the sample mean. Find the mean, variance, and standard deviation for the sample mean.
c.) suppose a random sample of size 3 is selected from this population without replacement. Find the sampling distribution of the sample median. Find the mean, variance, and standard deviation for the sample median.
d.) compare the mean of the sample mean with the population mean. Compare the mean of the sample median with the population median.
Explanation / Answer
The Sports Authority sells five different medicine balls with weights (in kilograms) given below:
10 12 15 18 25
a.) Find the population mean and the population median.
Descriptive statistics
data
n
5
mean
16.0000
median
15.00
population variance
27.6000
population standard deviation
5.2536
b.) Suppose a random sample of size 3 is selected from this population without replacement. Find the sample distribution of the sample mean. Find the mean, variance, and standard deviation for the sample mean.
Sample space
x1
x2
x3
mean
10
12
15
12.3333
10
12
18
13.3333
10
12
25
15.6667
10
15
18
14.3333
10
15
25
16.6667
10
18
25
17.6667
12
15
18
15.0000
12
15
25
17.3333
12
18
25
18.3333
15
18
25
19.3333
Descriptive statistics
mean
count
10
mean
16.0000
sample standard deviation
2.2608
sample variance
5.1111
minimum
12.3333
maximum
19.3333
range
7
c.) Suppose a random sample of size 3 is selected from this population without replacement. Find the sampling distribution of the sample median. Find the mean, variance, and standard deviation for the sample median.
Descriptive statistics
median
n
10
mean
15.00
sample standard deviation
2.45
sample variance
6.00
minimum
12
maximum
18
range
6
d.) Compare the mean of the sample mean with the population mean. Compare the mean of the sample median with the population median.
mean of the sample mean is 16 which is same as the population mean 16.
mean of the sample median is 15 which is same as the population median 15.
Descriptive statistics
data
n
5
mean
16.0000
median
15.00
population variance
27.6000
population standard deviation
5.2536
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