estimating a population proportion 100 150 words- Savvy Essay Writers | savvyessaywriters.net

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estimating a population proportion 100 150 words- Savvy Essay Writers | savvyessaywriters.net

Prompt

Harris Interactive® conducted a poll of American adults in August of 2011 to study the use of online medical information. Of the 1,019 randomly chosen adults, 60% had used the Internet within the past month to obtain medical information.

  1. Use the results of this survey to create an approximate 95% confidence interval estimate for the percentage of all American adults who have used the Internet to obtain medical information in the past month.
  2. Calculate the 90% confidence interval.
  3. Which confidence interval has the smaller margin of error? Why does this make sense?
  4. Which confidence interval is more likely to contain the true percentage of all American adults who have used the Internet to obtain medical information in the past month? Why do you think so?

ANSWER(S){ Hint }

Answer to Number 1: 95% confidence interval

LaTeX: hat{p}=0.60



p


^




=


0.60
 (60%) and LaTeX: n=1,019

n


=


1


,


019

Conditions: With such a large sample, we obviously have more than 10 successes and failures. There are (1019)(0.60) about 611 successes and (1019)(0.40) about 408 failures. So we can use the confidence interval formula.

Calculating the 95% confidence interval:

LaTeX: text{estimated standard error}=sqrt{frac{0.60left(1-0.60right)}{1019}}approx0.0153

estimated standard error


=





0.60



(


1


−


0.60


)




1019




≈


0.0153

LaTeX: text{sample proportion}pmtext{margin of error}

sample proportion


±


margin of error

0.60 ± 2 (0.015)

0.60 ± 0.030, which gives the interval 0.57 to 0.63

Answer to Number 2: 90% confidence interval

The only thing that changes is the margin of error. Instead of 2 standard errors, the 90% confidence interval has a margin of error equal to 1.65 standard errors.

0.60 ± 1.65(0.015)

0.60 ± 0.025, which gives the interval 0.575 to 0.625.

Answer to Number 3: Which has a smaller margin of error?

The 90% confidence has a smaller margin of error. We can see this in the calculations; the margin of error is 1.65 times the standard error instead of 2 times the standard error.

Answer to Number 4: Which is more likely to contain the population proportion?

The 95% confidence interval is more likely to contain the population proportion. The confidence level describes the chance (probability) that the associated confidence interval will contain the population proportion. With a 95% confidence interval, there is a 95% chance that the interval contains p; while the 90% confidence interval has a 90% chance of containing p.

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