Question

(plz type the answer)

8.24 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.9

(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

(a)

number of survey respondents reported that they consume five or more servings of soft drinks per week

0.16*2006 = 320.96 ≈ 321

Rounding to the nearest whole number was necessary because you can not have fractions of people.

(b)

95% confidence interval for the proportion of New Zealanders who report that they consume five or more servings of soft drinks per week.

z value for 95% is 1.96

95% CI for p

=0.16 - 1.96*sqrt(0.16*(1-0.16)/2006) , 0.16 + 1.96*sqrt(0.16*(1-0.16)/2006)

=0.16 - 0.01604 , 0.16 + 0.01604

=(0.1439 , 0.1760)

(c)

Converting the estimate and your confidence interval to percents.

estimate = 16%

confidence interval = (14.39% , 17.60%)

(d)

The estimate might be biased because the survey did not include people under 15 years of age.