Probability and Samples

Application 5

1 ) Briefly define each of the following

Distribution of sample means (refers to the collection of sample means for all the possible random samples of a particular size (n ) that can be obtained from a population

Expected value of M (refers to the value of a sample mean over time

Standard error of M (the standard deviation of the differences between the sample and population mean

2 ) For a sample selected from a population with a mean of u 50 and a standard deviation of o 10

a

. What is the expected value of M and the standard error of M for a sample of n 25

scores

EM 50

SEM 2

b . What is the expected value of M and the standard error of M for a sample of n 25

scores

EM 50

SEM 2

3 ) A population has a mean of u 80 and a standard deviation of o 10

a . If you selected a random sample of n 4 scores from this population , how much

error would you expect between the sample mean and the population mean

SEM 5

4 ) A population forms a normal distribution with a mean of u 75 and a standard

deviation of o 20

Sketch the distribution of sample means for samples of n 25 from this population xxx

59 .0

63 .0

67 .0

71 .0

75 .0

79 .0

83 .0

87 .0

91 .0

Sample Mean n 25 Sample Means from 75 to left and right

Left Right

[at Msource 75]

74 .6 75 .4

74 .2 75 .8

73 .8 76 .2

73 .4 76 .6

73 77

72 .6 77 .4

72 .2 77 .8

71 .8 78 .2

71 .4 78 .6

71 79

70 .6 79 .4

70 .2 79 .8

69 .8 80 .2

69 .4 80 .6

69 81

68 .6 81 .4

68 .2 81 .8

67 .8 82 .2

67 .4 82 .6

67 83

66 .6 83 .4

66 .2 83 .8

65 .8 84 .2

65 .4 84 .6

65 85

64 .6 85 .4

64 .2 85 .8

63 .8 86 .2

63 .4 86 .6

63 87

62 .6 87 .4

62 .2 87 .8

61 .8 88 .2

61 .4 88 .6

61 89

60 .6 89 .4

60 .2 89 .8

59 .8 90 .2

59 .4 90 .6

59 91

What proportion of the sample means for n 25 have values less than 80 In other words , Find

(M 80 ) for n 25

p (M 80 .05

5 ) A normal-shaped distribution has u 80 and o 15

Sketch the distribution of sample means for samples of n 25 scores from this

population

xxx

68 .0

71 .0

74 .0

77 .0

80 .0

83 .0

6 .0

9 .0

92 .0

Sample Mean n 25 Sample Mean where n 25 , mean 80

Left Right

[at Msource 80]

79 .7 80 .3

79 .4 80 .6

79 .1 80 .9

78...