Question

	80%	90%	95%	98%	99%
Mean	70611.96	70611.96	70611.96	70611.96	70611.96
Z score	1.28	1.64	1.96	2.33	2.58
Standard Error	1516.38	1516.38	1516.38	1516.38	1516.38
Margin of Error	1943.32	2494.22	2972.05	3527.63	3905.93
Lower CI	68668.64	68117.74	67639.91	67084.34	66706.03
Upper CI	72555.28	73106.18	73584.01	74139.59	74517.90

What trend do you see takes place to the confidence interval as the confidence level rises? Explain mathematically why that takes place.

Answer 1

Using the given data, we can see that the z score and margin of error are changing or we can say increasing for each confidence interval from 80% to 99% and this resulted in wider confidence interval width moving from 80% to 99%.

We know that the margin of error = z*(standard error)

so, it is clear that as z critical value increases with confidence level, the margin of error is also increasing.

Confidence interval width for 80% = upper limit - lower limit

= 72555.28 - 68668.64

= 3886.64

and

confidence interval width for 90% = upper limit - lower limit

= 73106.18-68117.74

= 4988.44

similarly, the confidence interval width for 99% = upper limit - lower limit

= 74517.90- 66706.03

= 7811.87

therefore, we can say that the trend is showing increase in width with increase in confidence level