Question

Write a discussion post :

As we have seen, a confidence interval is constructed using the form

point estimate±critical value×standard error

where the point estimate is the value calculated from the sample (e.g. a sample mean), the critical value is a cutoff value from the normal distribution, and the standard error measures the variability of sample means. The margin of error is the second part of this formula:

critical value×standard error

which indicates our uncertainty in the estimate.

Confidence intervals are ubiquitous in scientific articles, but they are also common in reporting some types of general news, although they are usually not labeled as "confidence intervals". If you have ever seen the results of a political poll, you may have noticed that along with the main result the polls generally report a margin of error as well.

For this week's post, find a value that is reported in a news source or scientific article using a margin of error. Briefly describe the quantity being estimated, and find the standard error by dividing the margin of error by the critical value (if a confidence level is reported, use that confidence level and qnorm to find the critical value; otherwise, you may assume 95% confidence). What does the standard error tell you about the variability of this estimate?

If you are having trouble finding a value reported with a margin of error, try looking at any news source reporting political polls, or a data-oriented news source such as FiveThirtyEight.

Answer 1

Sol:

here we have taken data

from

link is:

https://projects.fivethirtyeight.com/trump-approval-ratings/

population proportion who disapprove Donald trump is

p=0.528

point estimate=0.528

z crit for 95%=1.96

margin of error =zcrit*sqrt(p*(1-p)/n

given till day 798

so n=798

margin of error =1.96*sqrt(0.528*(1-0.528)/798)=0.03464

95% confidence interval for true population proportion of voters who disagree trump is

point estimate-margin of error,point estimate+margin of error

0.528-0.03464,0.528+0.03464

0.49336,0.56264

0.49336*100,0.56264*100

=49.3%,56.3%

we are 95% confident that the true population proportion of voters who disagree trump lies in between

49.3% to 56.3%