Answer with explanation:
Given : Sample size : n=425
The proportion of the population in Category A : ![0.27](https://tex.z-dn.net/?f=0.27)
Significance level : ![\alpha=1-0.95=0.05](https://tex.z-dn.net/?f=%5Calpha%3D1-0.95%3D0.05)
Critical value : ![z_{\alpha/2}=1.96](https://tex.z-dn.net/?f=z_%7B%5Calpha%2F2%7D%3D1.96)
Since in normal distribution, the best estimate for proportion for population p is equals to the proportion for the sample.
Thus ,the best point estimate for p =0.27
Formula for margin of error :-
![E=z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}\\\\=(1.96)\sqrt{\dfrac{0.27(1-0.27)}{425}}\\\\=0.0422089859404\approx0.0422](https://tex.z-dn.net/?f=E%3Dz_%7B%5Calpha%2F2%7D%5Csqrt%7B%5Cdfrac%7Bp%281-p%29%7D%7Bn%7D%7D%5C%5C%5C%5C%3D%281.96%29%5Csqrt%7B%5Cdfrac%7B0.27%281-0.27%29%7D%7B425%7D%7D%5C%5C%5C%5C%3D0.0422089859404%5Capprox0.0422)
Hence, the margin of error = 0.0422
Now, the confidence interval for population proportion is given by :-
![p\pm E \\\\=0.27\pm0.0422\\\\=(0.27-0.0422,\ 0.27+0.0422)\\\\=(0.2278,\ 0.3122)](https://tex.z-dn.net/?f=p%5Cpm%20E%20%5C%5C%5C%5C%3D0.27%5Cpm0.0422%5C%5C%5C%5C%3D%280.27-0.0422%2C%5C%200.27%2B0.0422%29%5C%5C%5C%5C%3D%280.2278%2C%5C%200.3122%29)
Hence, the 99% confidence interval for the proportion of the population in Category A given that 27% of a sample of 425 are in Category A = ![(0.2278,\ 0.3122)](https://tex.z-dn.net/?f=%280.2278%2C%5C%200.3122%29)
Answer:
B
Step-by-step explanation:
A cubic function begins with an X^3.
Answer:
Hi there!
She used <u>rounding</u> to estimate the sum!
So when multiplying or dividing, students can use a fact from the inverse operation. ... In multiplication the numbers you multiply are called factors; the answer is called the product. In division the number being divided is the dividend, the number that divides it is the divisor, and the answer is the quotient.