A survey commissioned by a health care group reported that 16% of New Zealanders

Question

A survey commissioned by a health care 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 2,005 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? (Round your answer to the nearest whole number.)

(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. (Round your answers to four decimal places.)

(c) Convert the estimate and your confidence interval to percents. (Round your answers to two decimal places.)

(d) Discuss reasons why the estimate might be biased. (Select all that apply.)

The survey was commissioned by a health care group.

The survey respondents might have lied.

The survey only included New Zealanders.

The survey had 2,005 people.

The survey did not include people under 15 years of age.

The survey questions may have been biased.

Explanation / Answer

a)
Number of respondents who report that they consume five or more servings of soft drinks per week, = 16%*2005 = 320.8 i.e. 321

b)
p = 0.16
n = 2005
SE = sqrt(p*(1-p)/n) = sqrt(0.16*0.84/2005) = 0.0082
z-value for 95%, = 1.96
ME = z*SE = 1.96*0.0082 = 0.0161

Confidence interval = (p - ME, p + ME)
= (0.16 - 0.0161, 0.16 + 0.0161)
= (0.144, 0.1761)

c)
Confidence interval in percent = (14.4%, 17.61%)

d)
The survey question may have been biased.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.