Question

Soft drink consumption in New Zealand. A survey commissioned by the Southern Cross Healthcare Group reported that 16% of New Zealanders consume five or more servings of soft drinks per week. The data were obtained by an online survey of 2006 randomly selected New Zealanders over 15 years of age.a) What number of survey respondents reported that they consume five or more servings of soft drinks per week? You will need to round your answer. Why? b) Find a 95% confidence interval for the proportion of New Zealanders who report that they consume five or more servings of soft drinks per week. c) Convert the estimate and your confidence interval to percents. d) Discuss reasons why the estimate might be biased.

Answer 1

Answer with explanation:

Given : The proportion of New Zealanders consume five or more servings of soft drinks per week :
`\hat{p}= 0.16`

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{\frac{\hat{p}(1-\hat{p})}{n}}`

, where
`\hat{p}` = Sample proportion.

n= Sample size.

z* = Critical value.

For n= 2006 ,
`\hat{p}= 0.16` and critical value for 95% confidence interval : z* = 1.96

Then , the required confidence interval will be :

`0.16\pm (1.96)\sqrt{( 0.16(1- 0.16))/(2006)}`

`0.16\pm (1.96)√( 0.000066999002991)`

`0.16\pm (1.96)(0.00818529186963)`

`0.16\pm 0.0160431720645`

`(0.16-0.0160431720645,\ 0.16+0.0160431720645)`

`(0.143956827935,\ 0.176043172064)\approx(0.144,\ 0.176)`

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)`

c)
`(0.144,\ 0.176)=(0.144*100\%,\ 0.176*100\%)`

`=(14.4\%,\ 17.6\%)`176\times100\%)[/tex]

d) The estimate might be biased because the survey is taken online that means offline New Zealanders are out of consideration.