Memo
Calculations on Confidence intervals
8.5
Z = standard normal variable (x-u) = 65.83-64 = 1.83
σ = population standard deviation = 13.61
μ= Arithmetic mean or average of a population = 65.83
n = size of the population = 20
=
= 65.83 + 26.9379 = 92.7679
= 65.83 – 26.7679 = 39.0621
Confidence interval = (39.0621, 92.7679)
= 65.83 + 5.5693 = 71.3993
= 65.83 – 5.5693 = 60.2607
Confidence interval = (60.2607, 71.3993)
S=standard deviation = 13.61, n = 20, x = 65.83,
= 0.2236
= 65.83 0.6805
= 65.83 + 0.6805 = 66.5105
= 65.83 – 0.6805 = 65.1495
Confidence interval = (65.1495, 66.5105)
The confidence levels vary when we use different values of standard deviations. Therefore, the conclusions made in week 4 would change in order to accommodate economic and funding factors affecting education. Confidence interval in this case quantifies the uncertainty of business opportunities in the education sector by presenting upper and lower limits of student populations. The largest confidence interval is found in the first case where the actual values of σ are used. Three factors impact on the confidence interval: Sample size, population size and percentage (Black, 1999). A gap exists in the educational sector due to poverty and the government’s priority on other sectors such as healthcare (Parekh, Killoran & Crawford, 2011). According to Sekaran (2003), the confidence level interval increases as the interval spreads. In other words as sample size increases, the interval narrows in order to represent the entire population.
References
Black, T. (1999). Doing quantitative research in the social sciences:An integrated approach
to research design, measurement, and statistics. Thousand Oaks, CA: SAGE
Publications, Inc.
Parekh, G., Killoran, I. & Crawford, C. (2011). The Toronto Connection: Poverty, Perceived
Ability and Access to Education Equity. Canadian Journal Of Education, 34(3), 249- 279.
Sekaran, U. (2003). Research Methods for Business. A Skill-Building Approach, (4th
Edition) London: Wiley, Inc. A Pearson Education Company.
