Question

Sample information: 24 out of 1000 people who were surveyed had type 2 diabetes. Use the above sample information and construct two confidence intervals (one with confidence level of 90% and the other one with confidence level of 99%) to estimate the proportion of people who have type 2 diabetes. What is the relationship between the confidence level and the size of the confidence interval? Is this significant? Why is it important to understand this concept?

Answer 1

(a)

To construct 90% Confidence Interval:

n = Sample Size = 1000

p = Sample Proportion = 24/1000 = 0.024

q = 1 - p = 0.976

= 0.10

From Table, critical values of Z = 1.645

90% Confidence Interval:

0.024 (1.645 X 0.004840)

= 0.024 0.007962

= ( 0.0160 ,0.0320)

90% Confidence Interval:

0.0160 < P <   0.0320

(b)

To construct 99% Confidence Interval:

n = Sample Size = 1000

p = Sample Proportion = 24/1000 = 0.024

q = 1 - p = 0.976

= 0.01

From Table, critical values of Z = 2.576

99% Confidence Interval:

0.024 (2.576 X 0.004840)

= 0.024 0.0125

= ( 0.0115 ,0.0365)

99% Confidence Interval:

0.0115 < P <   0.0365

(c)

The width of the Confidence Interval increases as the Confidence Level increases. It is important to understand this concept because the greater the confidence level, the wider the confidence interval.and so, this relationship is made use of for selecting confidence level to meet the desired width of the Confidence Interval