Assignment 5



Assignment 5

Question 1

Test Score

Z equivalent

Percentile Position

Transformed T Scores

25

2.6667

68.0000

76.667

24

2.3333

70.8333

73.333

23

2

73.9130

70.000

22

1.6667

77.2727

66.667

21

1.3333

80.9524

63.333

20

1

85.0000

60.000

19

0.6667

89.4737

56.667

18

0.3333

94.4444

53.333

17

0.0000

100.0000

50.000

16

-0.3333

106.2500

46.667

15

-0.6667

113.3333

43.333

Question 2



Mean

101.1667

Std. Dev

12.2082



Pretest scores

Z - scores

Percentile Ranks

90

-0.93083

88.95917762

93

-0.68083

91.92448354

94

-0.5975

92.91291885

98

-0.26417

96.86666008

125

1.985833

123.5544134

95

-0.51417

93.90135416

100

-0.0975

98.84353069

104

0.235833

102.7972719

106

0.4025

104.7741425

110

0.735833

108.7278838

75

-2.18083

74.13264802

88

-1.0975

86.98230701

90

-0.93083

88.95917762

105

0.319167

103.7857072

120

1.569167

118.6122368

80

-1.76417

79.07482455

100

-0.0975

98.84353069

105

0.319167

103.7857072

110

0.735833

108.7278838

119

1.485833

117.6238015

95

-0.51417

93.90135416

99

-0.18083

97.85509538

104

0.235833

102.7972719

110

0.735833

108.7278838

120

1.569167

118.6122368

85

-1.3475

84.01700109

90

-0.93083

88.95917762

100

-0.0975

98.84353069

110

0.735833

108.7278838

115

1.1525

113.6700603

d..

i. 20%

ii. 30%

iii. 66.67%

iv. 33.33%

v. 110

vi. 125

Question 3

 

Pretest scores

Posttest scores

Pretest scores

1

Posttest scores

0.866110757

1

75.01% of the linear association present in pretest and posttest scores.

R - square

0.750147844



Question 4

The results of the above equation shows that if there is no difference on the control group i.e. pretest score obtained is 0, still the student will get 45 marks. The slope coefficient shows that with every increase in the pretest score, there is 64.2% change in posttest scores.



Standard Error

Pretest scores

2.228903

Posttest scores

1.5956



y = 0.642*105 + 45 = 112.41

Question 5



H0: There is no significant difference in the mean pretest and posttest IQ scores for the control group.

HA: There is a significant difference in the mean pretest and posttest IQ scores for the control group.



H0: There is no significant difference of pretest and Posttest IQ scores (Bloomers).

HA: There is a significant difference of pretest and Posttest IQ scores (Bloomers).

Question 6

Population distribution and sampling distribution of means

Sampling can be done with or without replacement, and the starting population can be infinite or finite. A finite population in which sampling is performed with replacement can be considered theoretically infinite. Also, for practical purposes, a very large population can be considered infinite. Throughout our study we will limit ourselves to an infinite base population or sampling with replacement. Consider all possible samples of size n in a population. For each sample one can calculate statistics (mean, standard deviation, ratio, etc) which varies from one to another. Thus we obtain a statistical distribution called sampling distribution.

Interval Estimate of a population mean

The "interval estimate" is to determine a pair of values ??a and b, such that constituted interval [a, b], and for a probability 1 - default (level trust) is verified with respect to the parameter to be estimated compliance.

Standard Error of mean

Standard error is the standard deviation of the sampling distribution of a statistic. The term also refers to an estimate of the standard deviation derived from a particular sample used to compute the estimate.

Central limit theorem

The central limit theorem is a mathematical theorem saying that if X and are independent random variables with the same schedule, the same expected value and finite variance, the random variable of the form

Converges by the distribution to a standard normal distribution when increases to infinity.

Statistical Inference

Statistical inference is a branch of statistics dealing with the problems of generalizing the results of the study of the random sample to the entire population, and the estimation errors resulting from such generalizations. There are two groups of methods generalizing the results, at the same time defining the two sections of statistical inference:

Estimating - estimating the value of unknown parameters.

Verification of statistical hypotheses - validating assumptions about the distribution.



The size of the pretest and posttest results has been placed on the horizontal axis because the size is an independent variable. The independent variables are placed on the horizontal axis and the response variables are placed ...