Answer:
The 98% confidence interval for population proportion of people who refuse evacuation is {0.30, 0.33].
Step-by-step explanation:
The sample drawn is of size, <em>n</em> = 5046.
As the sample size is large, i.e. <em>n</em> > 30, according to the Central limit theorem the sampling distribution of sample proportion will be normally distributed with mean
and standard deviation
.
The mean is: 
The confidence level (CL) = 98%
The confidence interval for single proportion is:
![CI_{p}=[\hat p-z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} },\ \hat p+z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} }]](https://tex.z-dn.net/?f=CI_%7Bp%7D%3D%5B%5Chat%20p-z_%7B%28%5Calpha%20%2F2%29%7D%5Ctimes%5Csqrt%7B%5Cfrac%7B%5Chat%20p%20%281-%5Chat%20p%29%7D%7Bn%7D%20%7D%2C%5C%20%5Chat%20p%2Bz_%7B%28%5Calpha%20%2F2%29%7D%5Ctimes%5Csqrt%7B%5Cfrac%7B%5Chat%20p%20%281-%5Chat%20p%29%7D%7Bn%7D%20%7D%5D)
Here
= critical value and <em>α </em>= significance level.
Compute the value of <em>α</em> as follows:

For <em>α</em> = 0.02 the critical value can be computed from the <em>z</em> table.
Then the value of
is ± 2.33.
The 98% confidence interval for population proportion is:
![CI_{p}=[\hat p-z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} },\ \hat p+z_{(\alpha /2)}\times\sqrt{\frac{\hat p (1-\hat p)}{n} }]\\=[0.31-2.33\times \sqrt{\frac{0.31\times(1-0.33)}{5046} },\ 0.31+2.33\times \sqrt{\frac{0.31\times(1-0.33)}{5046} } ]\\=[0.31-0.0152,\ 0.31+0.0152]\\=[0.2948,0.3252]\\\approx[0.30,\ 0.33]](https://tex.z-dn.net/?f=CI_%7Bp%7D%3D%5B%5Chat%20p-z_%7B%28%5Calpha%20%2F2%29%7D%5Ctimes%5Csqrt%7B%5Cfrac%7B%5Chat%20p%20%281-%5Chat%20p%29%7D%7Bn%7D%20%7D%2C%5C%20%5Chat%20p%2Bz_%7B%28%5Calpha%20%2F2%29%7D%5Ctimes%5Csqrt%7B%5Cfrac%7B%5Chat%20p%20%281-%5Chat%20p%29%7D%7Bn%7D%20%7D%5D%5C%5C%3D%5B0.31-2.33%5Ctimes%20%5Csqrt%7B%5Cfrac%7B0.31%5Ctimes%281-0.33%29%7D%7B5046%7D%20%7D%2C%5C%200.31%2B2.33%5Ctimes%20%5Csqrt%7B%5Cfrac%7B0.31%5Ctimes%281-0.33%29%7D%7B5046%7D%20%7D%20%5D%5C%5C%3D%5B0.31-0.0152%2C%5C%200.31%2B0.0152%5D%5C%5C%3D%5B0.2948%2C0.3252%5D%5C%5C%5Capprox%5B0.30%2C%5C%200.33%5D)
Thus, the 98% confidence interval [0.30, 0.33] implies that there is a 0.98 probability that the population proportion of people who refuse evacuation is between 0.30 and 0.33.