Question

ACCORDING TO THE FEBRUARY 2008 FEDERAL trade commission reports on consumer fraud and identity theft, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints. Calculate 90% confidence interval

Answer 1

Answer:  (0.205905, 0.242095)

Step-by-step explanation:

We know that the confidence interval for population proportion is given by :-

$\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}$

, where $\hat{p}$= sample proportion

n= sample size

Let p be the proportion of complaints of identity theft .

As per given , we have

n= 1432

$\hat{p}=\dfrac{321}{1432}\approx0.224$

By standard normal table , z* = 1.645 for 90% confidence level.

Now , 90% confidence interval for p will be :

$0.224\pm (1.645)\sqrt{\dfrac{0.224(1-0.224)}{1432}}\\\\=0.224\pm (1.645)(0.011)\\\\=0.224\pm 0.018095\\\\=(0.224-0.018095,\ 0.224+0.018095)\\\\=(0.205905,\ 0.242095)$

Hence, required confidence interval = (0.205905, 0.242095)