statistics z table


A simple random sample is defined as one in which each element of the population has an equal and independent chance of being selected. In case of a population with N units, the probability of choosing n sample units, with all possible combinations of NCn samples is given by 1/NCn e.g. If we have a population of five elements (A, B, C, D, E) i.e. N 5, and we want a sample of size n = 3, then there are 5C3 = 10 possible samples and the probability of any single unit being a member of the sample is given by 1/10.

Simple random sampling can be done in two different ways i.e. ‘with replacement’ or ‘without replacement’. When the units are selected into a sample successively after replacing the selected unit before the next draw, it is a simple random sample with replacement. If the units selected are not replaced before the next draw and drawing of successive units are made only from the remaining units of the population, then it is termed as simple random sample without replacement. Thus in the former method a unit once selected may be repeated, whereas in the latter a unit once selected is not repeated. Due to more statistical efficiency associated with a simple random sample without replacement it is the preferred method.

A simple random sample can be drawn through either of the two procedures i.e. through lottery method or through random number tables.

  • Lottery Method – Under this method units are selected on the basis of random draws. Firstly each member or element of the population is assigned a unique number. In the next step these numbers are written on separate cards which are physically similar in shape, size, color etc. Then they are placed in a basket and thoroughly mixed. In the last step the slips are taken out randomly without looking at them. The number of slips drawn is equal to the sample size required.Lottery method suffers from few drawbacks. The process of writing N number of slips is cumbersome and shuffling a large number of slips, where population size is very large, is difficult. Also human bias may enter while choosing the slips. Hence the other alternative i.e. random numbers can be used.
  • Random Number Tables Method – These consist of columns of numbers which have been randomly prepared. Number of random tables are available e.g. Fisher and Yates Tables, Tippets random number etc. Listed below is a sequence of two digited random numbers from Fisher & Yates table:61, 44, 65, 22, 01, 67, 76, 23, 57, 58, 54, 11, 33, 86, 07, 26, 75, 76, 64, 22, 19, 35, 74, 49, 86, 58, 69, 52, 27, 34, 91, 25, 34, 67, 76, 73, 27, 16, 53, 18, 19, 69, 32, 52, 38, 72, 38, 64, 81, 79 and 38.

    The first step involves assigning a unique number to each member of the population e.g. if the population comprises of 20 people then all individuals are numbered from 01 to 20. If we are to collect a sample of 5 units then referring to the random number tables 5 double digit numbers are chosen. E.g. using the above table the units having the following five numbers will form a sample: 01, 11, 07, 19 and 16. If the sampling is without replacement and a particular random number repeats itself then it will not be taken again and the next number that fits our criteria will be chosen.

Thus a simple random sample can be drawn using either of the two procedures. However in practice, it has been seen that simple random sample involves lots of time and effort and is impractical.


Table of Contents
1.statistics adjusted rsquared

2.statistics analysis of variance

3.statistics arithmetic mean

4.statistics arithmetic median

5.statistics arithmetic mode

6.statistics arithmetic range

7.statistics bar graph

8.statistics best point estimation

9.statistics beta distribution

10.statistics binomial distribution

11.statistics blackscholes model

12.statistics boxplots

13.statistics central limit theorem

14.statistics chebyshevs theorem

15.statistics chisquared distribution

16.statistics chi squared table

17.statistics circular permutation

18.statistics cluster sampling

19.statistics cohens kappa coefficient

20.statistics combination

21.statistics combination with replacement

22.statistics comparing plots

23.statistics continuous uniform distribution

24.statistics cumulative frequency

25.statistics coefficient of variation

26.statistics correlation coefficient

27.statistics cumulative plots

28.statistics cumulative poisson distribution

29.statistics data collection

30.statistics data collection questionaire designing

31.statistics data collection observation

32.statistics data collection case study method

33.statistics data patterns

34.statistics deciles statistics

35.statistics dot plot

36.statistics exponential distribution

37.statistics f distribution

38.statistics f test table

39.statistics factorial

40.statistics frequency distribution

41.statistics gamma distribution

42.statistics geometric mean

43.statistics geometric probability distribution

44.statistics goodness of fit

45.statistics grand mean

46.statistics gumbel distribution

47.statistics harmonic mean

48.statistics harmonic number

49.statistics harmonic resonance frequency

50.statistics histograms

51.statistics hypergeometric distribution

52.statistics hypothesis testing

53.statistics interval estimation

54.statistics inverse gamma distribution

55.statistics kolmogorov smirnov test

56.statistics kurtosis

57.statistics laplace distribution

58.statistics linear regression

59.statistics log gamma distribution

60.statistics logistic regression

61.statistics mcnemar test

62.statistics mean deviation

63.statistics means difference

64.statistics multinomial distribution

65.statistics negative binomial distribution

66.statistics normal distribution

67.statistics odd and even permutation

68.statistics one proportion z test

69.statistics outlier function

70.statistics permutation

71.statistics permutation with replacement

72.statistics pie chart

73.statistics poisson distribution

74.statistics pooled variance r

75.statistics power calculator

76.statistics probability

77.statistics probability additive theorem

78.statistics probability multiplicative theorem

79.statistics probability bayes theorem

80.statistics probability density function

81.statistics process capability cp amp process performance pp

82.statistics process sigma

83.statistics quadratic regression equation

84.statistics qualitative data vs quantitative data

85.statistics quartile deviation

86.statistics range rule of thumb

87.statistics rayleigh distribution

88.statistics regression intercept confidence interval

89.statistics relative standard deviation

90.statistics reliability coefficient

91.statistics required sample size

92.statistics residual analysis

93.statistics residual sum of squares

94.statistics root mean square

95.statistics sample planning

96.statistics sampling methods

97.statistics scatterplots

98.statistics shannon wiener diversity index

99.statistics signal to noise ratio

100.statistics simple random sampling

101.statistics skewness

102.statistics standard deviation

103.statistics standard error se

104.statistics standard normal table

105.statistics statistical significance

106.statistics formulas

107.statistics notations

108.statistics stem and leaf plot

109.statistics stratified sampling

110.statistics student t test

111.statistics sum of square

112.statistics tdistribution table

113.statistics ti 83 exponential regression

114.statistics transformations

115.statistics trimmed mean

116.statistics type i amp ii errors

117.statistics variance

118.statistics venn diagram

119.statistics weak law of large numbers

120.statistics z table

121.discuss statistics


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