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 2,004 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.)

Why was it necessary to round your answer in the previous question?     

    (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.

Explanation / Answer

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 2,004 randomly selected New Zealanders over 15 years of age.

We are given the sample size = n = 2004

Proportion of respondents that they consume five or more servings of soft drinks per week is given as 16%.

Required number of respondents = 2004*16% = 2004*0.16 = 320.64

Required number of respondents = 321

Why was it necessary to round your answer in the previous question?    

It is necessary to round the answer in the previous question as we know that the number of respondents always be an integer 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.)   

Solution:

We are given

Sample size = n = 2004, p = 0.16, confidence level = 95%

The formula for confidence interval is given as below:

Confidence interval = p -/+ z*sqrt(pq/n)

Where q = 1 – p = 1 – 0.16 = 0.84

Critical value Z = 1.96

Confidence interval = 0.16 -/+ 1.96*sqrt(0.16*0.84/2004)

Confidence interval = 0.16 -/+ 1.96*0.008189

Confidence interval = 0.16 -/+ 0.0161

Lower limit = 0.16 – 0.0161 = 0.1439

Upper limit = 0.16 + 0.0161 = 0.1761

Confidence interval = (0.1439, 0.1761)

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

Answer:

Confidence interval = (14.39%, 17.61%)

(d) Discuss reasons why the estimate might be biased.

Answer:

Estimate might be biased because the collected information is based on the online survey and there would be possibility of missing the participation of entire individuals in the country. Also, participants would not interest to respond the online survey most of the times.

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