Question

There are 169 million registered voters in the us. determine an interval for the number (how many) of registered democrats in the population. + answer

Answer 1

Part A:

Given that in a sample of 400 registered voters, 204 were democrats, i.e. n = 400,
`\hat{p}= (204)/(400) =0.51`

The 95% confidence interval for the proportion of registered democrats voters in the population is given by:


`95\%\ C.I.=\hat{p}\pm z_(\alpha/2)\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\ \\ =0.51\pm1.96\sqrt{(0.51(1-0.51))/(400)}=0.51\pm1.96\sqrt{(0.2499)/(400)} \\ \\ =0.51\pm1.96(0.025)=0.51\pm0.049=(0.51-0.049,\ 0.51+0.049) \\ \\ =\bold{(0.461,\ 0.559)}`



Part B:

Given that there are 169 million registered voters in the US, the interval for the number of registered democrats in the population is given by

[0.461(169,000,000), 0.559(169,000,000)] = (77,909,000, 94,471,000)