Mathematics Homework Help

1. A random sample of 5 year old children is evaluated for being left- or right-handed. The sample size is n = 100 children of which 79 are right-handed, 15 are left-handed, and 6 use both hands equally. According to genetic analyses, the expression of the dominant gene for handedness is highly correlated with actual handedness. Test the following hypothesis based on the sample given above at a significance level of α = 0.05. (5 marks)

   H0: p1= p2= p3= 0.33;

   H1: at least two of the probabilities are not the same

2. The distribution of grades for various classes taught by different professors is given in the following table. Test the null hypothesis that the grade distributions are homogenous for these three professors at a significance level of α = 0.05. (11 marks)

	Professor
Grade	Einstein	Rutherford	Bohr
A	18	36	20
B	25	44	15
C	85	73	82
D	17	12	8

1. Define in your own words the following words: (4 marks)
   1. Sensitivity
   2. Specificity
   3. Accuracy
   4. Test of homogeneity
2. Determine the sensitivity, specificity, and accuracy for the following analytical test data that detected the presence of morphine using the Marquis test. (5 marks)

			Expected results
			positive condition	negative condition
Actual morphine presence		positive outcome	15	2
		negative outcome	4	23

Would you conclude that the test is able to detect both true positive and true negative samples? Provide support for your answer.

After further consideration, the calculations will also need to be adjusted based on the correction. n21 and n12 need to be reversed as well when you adjust for the wrong location of the FP and FN notation.

I do apologize for this confusion and I will be extending the due date for Module 7 by a few days to allow time to adjust your assignment, if you desire. Please let me know if you have any questions.

Attached is a Word doc with a corrected chart that I hope will clarify things. I have seen many examples online where the values in the chart ore flipped, so you really have to be careful where the “actual” and “expected” or “predicted” words are located – rows or columns. In my research, I’ve found that this chart is, ironically, also called a “confusion” chart!

Keep in mind when looking at these charts that Actual is truth, Predicted (or Expected) is the test outcome. If you have a known positive that tests negative, this is a false negative. Conversely if you have a known negative that tests positive, this is a false positive.