Question

7. Alert nurses at the Veteran’s Affairs Medical Center in Northampton, Massachusetts, noticed an unusually high number of deaths when another nurse, Kristen Gilbert, was working. Those same nurses later noticed missing supplies of the drug epinephrine, which is a synthetic adrenaline that stimulates the heart. Kristen was arrested and charged with four counts of murder and two counts of attempted murder. When seeking a grand jury indictment, prosecutors provided a key evidence consisting of the table below. Use a 0.01 significance level to test the defense claim that deaths on shifts are independent of whether Gilbert was working. What does the result suggest about the guilt or innocence of Gilbert?

Shifts with a Death Shifts Without a Death

Gilbert Was Working 40 217

Gilbert Was Not Working 34 1350

Answer 1

Sol:

The objective is to test the defence claim that deaths on shift are independent of whether Gilbert was working.

Consider the null and alternative hypothesis as follows:

Null hypothesis:

The deaths on shifts are independent of whether Gilbert was working.

Alternative hypothesis:

The deaths on shifts and whether Gilbert was working are independent.

Let be the 1% level of significance.

The expected frequency for the cell (1, 1) is calculated as follows:

The expected frequencies are expressed in the following table.

Explanation | Hint for next step

Therefore, the expected frequencies were expressed in the following table,

	Shift with death	Without death	Total
Gilbert working	11.5893	245.4107	257
Not working	62.4107	1321.589	1384
Total	74	1567	1641

The test statistic used to test the hypothesis is,

Here, the ith observed frequency is represented by.

The ith expected frequency is represented by.

Construct the chi-square table using given data as follows:

Observed	Expected	Difference
40	11.5893	28.4107	69.6477
217	245.4107	-28.4107	3.2890
34	62.4107	-28.4107	12.9332
1350	1321.589	28.411	0.6108

Under the chi-square test statistic is,

Degrees of freedom:

The p-value of the test statistic is,

Since, p-value 0.0000 is less than the level of significance 0.01.

Therefore, there is an enough evidence to reject the null hypothesis.

If you Satisfy with Answer, Please give me "Thumb Up". It is very useful for me.
Thank you for your support.