Statistics Assignment: Statistical Analysis and Research Design

This statistics assignment addresses several key concepts in statistical analysis and research methods. The assignment begins with multiple-choice questions testing understanding of research types (descriptive, explanatory), research questions, and data analysis techniques. It then delves into central tendency, asking for calculations of the mean, median, and mode, and their interpretation. The assignment also covers confidence intervals and sampling errors, emphasizing the importance of these concepts in inferential statistics. It includes a discussion on the advantages and disadvantages of using the mean as a measure of central tendency and the impact of outliers and skewed data. The document also provides a detailed analysis of the data, including the calculation of mean, range, variance, standard deviation, and confidence intervals. Finally, it provides explanations of key statistical concepts and their practical applications in research, making it a comprehensive overview of statistical analysis techniques.

Question 1 – B
Question 2 – c
Question 3 – c
Question 4 – D
Question 5 – B
Question 6 – A
Question 7 – A
Question 8 – A
Question 9 – B
Question 10 – C
Question 11 – B
Question 12 – D
Question 13 – D
Question 14- C
Question 15 - D
Question 16 - B
Question 17 – B
Question 18- B
Question 19-
Question 20
Appropriate measure of central tendency

Age is mean (Value = 29.00)
Offense type is mode (Value = 3)
Mode of disposition is mode (Value = 7)
Sentence length is median (Value = 12)
Question 21
Mean = 92.91, Range = 577, Variance = 27489.29, Standard Deviation = 165.80
Question 22
95% CI = 25.92 ≤ μ ≤ 29.12
Question 23
1) One of the key benefits of using mean over other central tendency measures is that it is simpler
to compute and interpret. Another benefit is that the mean is a reliable estimator for the central
tendency especially for non-skewed data. Additionally, unlike other central tendency measures it
considers all the data values for the given variable and hence quicker and easy to implement.
2) In following circumstances, mean might lead to misleading conclusions.
 Instances where data contains outliers and hence the outlier would significantly impact
mean by distorting the same.
 Instances where data is skewed resulting in mean also being skewed
 Distributions where the data is non-numerical
Question 24
1) Sampling error arises on account of sample not being an accurate description of the underlying
population. It is imperative to consider confidence interval besides the point interval as
confidence interval provides us an interval with the requisite precision taking into account the
sampling error. Typically, the confidence interval is a more accurate estimation of the population
mean when compared with the point estimate.
2) It is imperative to note that confidence interval estimation is a inferential statistical technique
with the objective of parameter estimation based on sample. A key input used in confidence
interval estimation is the critical value which is essentially based on the underlying probability
distribution of the variable.