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

Answer 1

Solution :

The sample proportion $(\hat p)=\frac{24}{1000}$

                                           = 0.024

90% confidence interval

The standard deviation  = $\sqrt{\frac{\hat p(1-\hat p)}{n}$

                                        = $\sqrt{\frac{0.024(1-0.024)}{1000}$

                                        = 0.00484

z = 1.645 for 90% CI

Upper band = 0.024 + (0.00484 x 1.645 ) = 0.03196

Lower band = 0.024 - (0.00484 x 1.645 ) = 0.01603

Therefore, the 90% CI is (0.016, 0.032)

99% confidence interval

z = 2.576 for 99% CI

Upper band = 0.024 + (2.576 x 0.00484 ) = 0.0365

Lower band = 0.024 - (2.576 x 0.00484 ) = -0.0115

Therefore, the 99% CI is (0.0115, 0.0365)