<h2>
Answer with explanation:</h2>
Given : The proportion of New Zealanders consume five or more servings of soft drinks per week :![\hat{p}= 0.16](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%3D%200.16)
a) The number of survey respondents reported that they consume five or more servings of soft drinks per week = 2006
b) Confidence interval for population proportion (p) :
![\hat{p}\pm z^*\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}](https://tex.z-dn.net/?f=%5Chat%7Bp%7D%5Cpm%20z%5E%2A%5Csqrt%7B%5Cdfrac%7B%5Chat%7Bp%7D%281-%5Chat%7Bp%7D%29%7D%7Bn%7D%7D)
, where
= Sample proportion.
n= Sample size.
z* = Critical value.
For n= 2006 ,
and critical value for 95% confidence interval : z* = 1.96
Then , the required confidence interval will be :
![0.16\pm (1.96)\sqrt{\dfrac{ 0.16(1- 0.16)}{2006}}](https://tex.z-dn.net/?f=%200.16%5Cpm%20%281.96%29%5Csqrt%7B%5Cdfrac%7B%200.16%281-%200.16%29%7D%7B2006%7D%7D)
![0.16\pm (1.96)\sqrt{ 0.000066999002991}](https://tex.z-dn.net/?f=%200.16%5Cpm%20%281.96%29%5Csqrt%7B%090.000066999002991%7D)
![0.16\pm (1.96)(0.00818529186963)](https://tex.z-dn.net/?f=%200.16%5Cpm%20%281.96%29%280.00818529186963%29)
![0.16\pm 0.0160431720645](https://tex.z-dn.net/?f=%200.16%5Cpm%200.0160431720645)
![(0.16-0.0160431720645,\ 0.16+0.0160431720645)](https://tex.z-dn.net/?f=%280.16-0.0160431720645%2C%5C%200.16%2B0.0160431720645%29)
![(0.143956827935,\ 0.176043172064)\approx(0.144,\ 0.176)](https://tex.z-dn.net/?f=%280.143956827935%2C%5C%200.176043172064%29%5Capprox%280.144%2C%5C%200.176%29)
i.e. A 95% confidence interval for the proportion of New Zealanders who report that they consume five or more servings of soft drinks per week. = ![(0.144,\ 0.176)](https://tex.z-dn.net/?f=%280.144%2C%5C%200.176%29)
c) ![(0.144,\ 0.176)=(0.144\times100\%,\ 0.176\times100\%)](https://tex.z-dn.net/?f=%280.144%2C%5C%200.176%29%3D%280.144%5Ctimes100%5C%25%2C%5C%200.176%5Ctimes100%5C%25%29)
176\times100\%)[/tex]
d) The estimate might be biased because the survey is taken online that means offline New Zealanders are out of consideration.
Answer:
(-4, 0) U (1, ∞)
Step-by-step explanation:
Set each factor EQUAL to zero to find the zeroes (since it is not actually equal to zero, you will use an open circle when graphing and an open bracket when writing in interval notation).
x = 0 x-1 = 0 x + 4 = 0
x = 1 x = -4
Next, choose a value to the far left, between each of the zeroes, and to the far right to evaluate if it makes a true statement when input into the given inequality.
far left (I choose -5): -5(-5 - 1)(-5 + 4) > 0 → (-)(-)(-) > 0 → negative > 0 FALSE
- 4 to 0 (I choose -2): -2(-2 - 1)(-2 + 4) > 0 → (-)(-)(+) > 0 → positive > 0 TRUE
0 to 1 (I choose 0.5): .5(.5 - 1)(.5 + 4) > 0 → (+)(-)(+) > 0 → negative > 0 FALSE
far right (I choose 2): 2(2 - 1)(2 + 4) > 0 → (+)(+)(+) > 0 → positive > 0 TRUE
Answer:
-5 and 6
Step-by-step explanation:
-5 * 6 = -30
-5 + 6 = 1
<span>1, 4, 9, 16, and 25. Use the formula to get a2 = 1 + (2*2 - 1) = 4, a3 = 4 + (2*3 - 1) = 9, etc. Also notice that for all n, an = n2.</span>