Question

The following table summarizes the weights in kg of 40 students in this class

46 70 94 60

42 54 84 75

65 58 89 84

50 68 83 62

52 48 89 86

73 61 86 89

91 55 75 73

55 71 79 72

56 75 58 84

77 60 71 71

Determine a 10% random sample of the heights using the following three methods, and explain how you selected them. You may use a deck of cards, a random number table, RAND() in Excel or some other method to generate random numbers.

a. Random sampling

b. Systematic Random Sampling

c. Stratified Random Sampling

d. What is the sampling error for each method?

Answer 1

The average of the population data = sum of data / 40 = 69.775

>> a) Random sampling

sample = {83,73,70,71 } the sample is generated randomly using excel

sample mean = 74.25

d) sampling Error = 69.775 -  74.25 = - 4.475

>> b) Systematic Random Sampling

In this sampling method first, the data is ordered in increasing order and is rolled into a circle then a data point is selected at random then every kth data point is selected.

Here k = 40/4 = 10th

First data is chosen randomly in excel

sample = { 89,55,68,75 }

sample mean = 71.75

d) sampling Error = 69.775 -  71.75 = - 7.975

>>c) Stratified Random Sampling

In this method first, the data is sorted into increasing order then the data is divided into k stratum and each data point is taken randomly using excel fro each stratum

sample = {55,62,75,84 )

sample mean = 59

d) sampling Error = 69.775 -  69 = -0.775