Q2 [9 pts] Confidence level and margin of error.
A researcher wants to estimate the average weight of adult females in a certain population with a standard
deviation of 5kg. A random sample of 100 adult females is taken, and the average weight is found to be
65kg
(a) [6 pts] Determine three confidence intervals for the true mean weight of adult females in this
population, using 90%, 95%, and 99% confidence levels. Organize your steps by completing the
following table
Confidence level
90%
95%
99%
Z*
Margin of error = z* σ/√n
Interval: [Lower, upper]
1
(b) [1 pt] Based on the table obtained in part (a), how does increasing the confidence level change the
margin of error of a confidence interval when the sample size and population standard deviation
remain the same?
(c) [1 pt] Based on the table obtained in part (a), what can you conclude about the width of the
confidence interval at different confidence level? The width of the confidence interval measures
how wide the interval is, which can be calculated as Upper Limit - Lower Limit, the larger the
width, the wider the confidence interval.
(d) [1 pt] For the three different levels (90%, 95%, 99%) of confidence interval, if we increase the
sample size from 100 to 400, how would it change the margin of error?
Marking Rubric:
(a) 0.5 marks for each number in the tables, note that each CI has two numbers.
(b) 1 mark for the conclusion.
(c) 1 mark for the conclusion.
(d) 1 mark for the conclusion.
