Problem 6 (25 points) a. Bias is a tendency for a set of responses to read high
ID: 3232555 • Letter: P
Question
Problem 6 (25 points) a. Bias is a tendency for a set of responses to read high or low because of some inherent difficulty with the measurement process. Wi randomization in selecting the respondents help reduce potential bias related to sensitive questions? Will the respondents help reduce any potential bias? Explain your answer points) (5 b. When a few data points are repeated in a data set, the results are often arrayed in a frequency table. Consider the following data set: Score Frequency Proportion 3 0.64 0.16 2 0.08 o 3 i. Show how the average score can be calculated by using the frequencies (5 points) ii. Show how the average score could be calculated by using the proportions (5 points) deviation of the scores (5 points) iii. Calculate the standardExplanation / Answer
Part-A
Randomization will make the sensitive questions being equally asked to high or low response people and hence will reduce potential bias. Randomization make it possible to select individual without any regard to their property and so give equal opportunity to all individuals to be in the sample and hence will certainly reduce bias.
Part-B
Part-I Using frequency mean = Sum (xf)/Sum(f) = 58/25=2.32
Part-II Using proportions mean=Sum(xp) = 2.32
Part-III Standard deviation =sqrt[(x^2*p)-Mean2]=sqrt(6.48-2.322)=1.05
Score x
Frequency f
Proportion p
xf
xp
x^2*p
3
16
0.64
48
1.92
5.76
2
4
0.16
8
0.32
0.64
1
2
0.08
2
0.08
0.08
0
3
0.12
0
0
0
Total
25
1
58
2.32
6.48
Part-C
Precision and sampling error are inversely proportional. As the sampling error increase(or decrease) precision decreases(or increase) respectively.
As sampling error is inversely proportional to square root of sample size, so with small sample size , sampling error is higher and so precision is low while with large sample size, the sampling error will be low and so high precision
Score x
Frequency f
Proportion p
xf
xp
x^2*p
3
16
0.64
48
1.92
5.76
2
4
0.16
8
0.32
0.64
1
2
0.08
2
0.08
0.08
0
3
0.12
0
0
0
Total
25
1
58
2.32
6.48