Answer:
9
Step-by-step explanation:
<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: roughly 4.2593
Step-by-step explanation:
920/216
put the equation through a calculator
approx. 4.2593