Weather-Related Deaths For the most recent year as of this wri...

Question

Weather-Related Deaths For the most recent year as of this writing, the numbers of weather-related U.S. deaths for each month were 61, 14, 22, 26, 29, 42, 93, 49, 47, 35, 96, 16, listed in order beginning with January (based on data from the National Weather Service). Use a 0.01 significance level to test the claim that weather-related deaths occur in the different months with the same frequency. Provide an explanation for the result.

Accepted Answer

Hello. In this video, we are told that a hospital administrator records the number of emergency room visits for each shift in a day. The counts are 48 for the morning, 52 for the afternoon, 65 for the evening, and 35 for the night. At the 0.01 significance level, test the hypothesis that emergency room visits are distributed equally among the four shifts. So, let's go ahead and start this problem by setting up our hypothesis. Now, we want to test the claim that the emergency room visits are distributed equally among the 4 shifts. So our no hypothesis is going to be that the amount of emergency room visits. Are the same Amongst the different times of the day. And the alternate hypothesis is going to state the opposite, where the alternate hypothesis states that the emergency room visits are different amongst the different times of the day. So, in order to approach this problem, we are going to perform a G2 test. But in order to perform this test, the first thing we need to do is calculate the expected frequency of emergency room visits. So, in order to calculate the expected frequency, we are going to take the sum of the total amount of visits that were recorded in the day. That is going to be the sum of 4852. 65 and 35, and we will divide this by the amount of recordings that we've taken, which is going to be 4. This is going to give us an expected frequency of 50. Now, what we need to do for the G2 test is we need to calculate the different data points that we are going to enter for the G squared. Let's go ahead and look at an example of calculating a G score data point. OK, so here's an example of getting one value for the G square test. Now, What we are doing here is that we are looking at the morning data. We are going to take our observed piece of data, which is 48, and we are going to use our expected frequency, which we calculated to be 50. In order to get the first piece of the G score data, we are going to subtract the observed data from the expected frequency, so 48 minus 50 gives us -2. We will square that that frequency, which is going to give us 4, and divide that by the expected again. And 4 divided by 50 is going to give us 0.08. We are going to repeat this process for each time of the day, for afternoon, evening, and for night. And by repeating this process, we get that our Chi score statistic is equal to 0.08 plus 0.08 plus 4.50 plus 4.50. And that is going to give us a Chi score statistic of 9.16. So now what we want to do is we want to go ahead and calculate the critical value. We will set this statistic to the side for now. So, for the critical value, first, let's go ahead and find our degree of freedom. Now, the degree of freedom is going to be the amount of observations minus 1. So that is going to be 4-1, which gives us 3, and recall that we are working with a significance level of 0.01. So we want to find the G square critical value with respect to this degree of freedom and the significance level, and that is going to give us 11.345. Finally, we are going to compare our G square statistic to this critical value, but notice. That the chi square statistic is less than the chi squared critical value. What this means is that we fail. To reject Are no hypothesis. Which indicates that there's evidence to show that the ER visits are different. And with that being said, the solution to this problem is going to be A. So I hope this video helps you in understanding how to approach this problem, and we will go ahead and see you all in the next video.

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Key Concepts

Hypothesis Testing

Chi-Square Test

Significance Level

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