The following data gives the ages (in years) of all six members of a family 8 10

Question

The following data gives the ages (in years) of all six members of a family

8 10 12 50 55 69

a. Let X denote the age of a member of this family. Write the population probablility distribution of x and calculate the mean for the population data.

b. list all the possible sample of size two (without replacement) that can be selected from this population. Calculate the mean for each of these samples. Write the sampling distribution of the sample mean.

c. Select one of random samples of size 2 and compute the sampling error. Briefly explain the meaning of a sampling error.

d. Compare the mean of a population probability distribution with that of a sampling distribution.

e. Compare the dispersion in the population with that of the sample means.

Explanation / Answer

population mean={8+10+12+50+55+69}/6 =204/6 =34

population variance ={64+100+144+2500+3025+4761}/6 - {204*204}/6*6

=10594/6 -1156

=609.666

sd =27,048

all possible samplesof size 2 without replacement are

(8,10) ( 8,12) (8,50) (8,55) (8,69)

(10,12) (10,50) (10,55) (10,69)

(12,50) (12,55) (12,69)

(50,55) (50,69)

(55,69)

sample mean

since no sample mean is repeated frequency of each sample mean is 1

mean of sample means= 510/15 =34 =population mean

variance of sample means = 261.285

sd =16.164

variance of sample means < population variance

take first sample , here mean =9

population mean =34

sampling error = (34 -9) =25

8,10 9 8,12 10 8,50 29 8,55 31.5 8,69 38.5 10,12 11 10,50 30 10,55 32.5 10,69 39.5 12,50 31 12,55 33.5 12,69 40.5 50,55 52.5 50,69 59.5 55,69 62

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.