In the week before and the week after a holiday, there were 12,000 total deaths, and 5916 of them occurred in the week before the holiday. a. Construct a 95% confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week after the holiday b. Based on the result, does there appear to be any indication that people can temporarily postpone

Question

In the week before and the week after a holiday, there were 12,000 total deaths, and 5916 of them occurred in the week before the holiday. a. Construct a 95% confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week after the holiday b. Based on the result, does there appear to be any indication that people can temporarily postpone

their death to survive the holiday?

Answer 1

To construct a 95% confidence interval estimate of the proportion of deaths in the week before the holiday to the total deaths in the week before and the week after the holiday, we need to perform a proportion estimation.

a. First, let's calculate the proportion of deaths in the week before the holiday to the total deaths:

Proportion = Number of deaths in the week before the holiday / Total deaths

Proportion = 5916 / 12000

Proportion ≈ 0.493

Next, we will calculate the standard error of the proportion:

Standard Error = sqrt((Proportion * (1 - Proportion)) / n)

Where n is the total number of deaths: n = 12000

Standard Error = sqrt((0.493 * (1 - 0.493)) / 12000)

Standard Error ≈ 0.006

Now, to construct the confidence interval, we will use the formula:

Confidence Interval = Proportion ± (Z * Standard Error)

For a 95% confidence level, Z value is approximately 1.96 (from the standard normal distribution).

Confidence Interval = 0.493 ± (1.96 * 0.006)
Confidence Interval ≈ 0.493 ± 0.012

Therefore, the 95% confidence interval estimate of the proportion of deaths in the week before the holiday is approximately 0.481 to 0.505.

b. Based on the confidence interval, we cannot conclude that people can temporarily postpone their death to survive the holiday. The confidence interval does not indicate any significant evidence in favor or against this claim. Remember, the confidence interval provides an estimated range within which the true proportion of deaths could lie, and in this case, it does not show a significant change or pattern that suggests people are postponing their death to survive the holiday.