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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