Part A:
Given that in a sample of 400 registered voters, 204 were democrats, i.e. n = 400, <span>
![\hat{p}= \frac{204}{400} =0.51](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%20%5Cfrac%7B204%7D%7B400%7D%20%3D0.51)
</span>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{\frac{0.51(1-0.51)}{400}}=0.51\pm1.96\sqrt{\frac{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)}](https://tex.z-dn.net/?f=95%5C%25%5C%20C.I.%3D%5Chat%7Bp%7D%5Cpm%20z_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D%20%5C%5C%20%20%5C%5C%20%3D0.51%5Cpm1.96%5Csqrt%7B%5Cfrac%7B0.51%281-0.51%29%7D%7B400%7D%7D%3D0.51%5Cpm1.96%5Csqrt%7B%5Cfrac%7B0.2499%7D%7B400%7D%7D%20%5C%5C%20%20%5C%5C%20%3D0.51%5Cpm1.96%280.025%29%3D0.51%5Cpm0.049%3D%280.51-0.049%2C%5C%200.51%2B0.049%29%20%5C%5C%20%20%5C%5C%20%3D%5Cbold%7B%280.461%2C%5C%200.559%29%7D)
Part B:
Given that t<span>here
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)
</span>
Answer:
Pets Plus
Step-by-step explanation:
A 30% discount is greater than a 25% discount
Answer: 1) 2.059
2) 3.220
<u>Step-by-step explanation:</u>
1) log₆ 40
= log₆(5 x 8)
= log₆5 + log₆8
= 0.898 + 1.161
= 2.059
2) log₆ 320
= log₆ (40 x 8)
= log₆40 + log₆8
= 2.059 + 1.161
= 3.220