Answer:
And for this case the confidence interval is given by: (0.275, 0.305)
We can estimate the proportion difference as:
And the margin of error would be:
So then for this case the possibl two options are:
We are 95% confident that the true difference in proportion of Latinos who view global warming as a serious problem and whites who view global warming as a serious problem is 27.5% to 30.5%.
We are 95% confident that the difference between Latino and white opinions about the severity of global warming is 29% with a margin of error of 1.5%.
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the real population proportion of Latinos who view global warming as a serious problem
represent the estimated proportion Latinos who view global warming as a serious problem
is the sample size required of Latinos who view global warming as a serious problem
represent the real population proportion of white who view global warming as a serious problem
represent the estimated proportion of whitewho view global warming as a serious problem
is the sample size required of white
represent the critical value for the margin of error
Solution to the problem
The population proportion have the following distribution
The confidence interval for the difference of two proportions would be given by this formula
And for this case the confidence interval is given by: (0.275, 0.305)
We can estimate the proportion difference as:
And the margin of error would be:
So then for this case the possibl two options are:
We are 95% confident that the true difference in proportion of Latinos who view global warming as a serious problem and whites who view global warming as a serious problem is 27.5% to 30.5%.
We are 95% confident that the difference between Latino and white opinions about the severity of global warming is 29% with a margin of error of 1.5%.
