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 = 0.05. (5 points) H₀: p₁= p₂= p₃= 0.33; H₁: at least two of the probabilities are not the same

1. 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 = 0.05. (11 points)

Grade	Professor
	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 points)
   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 points)

	Predicted Outcome
Positive Condition	Negative Condition
Expected Outcome	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? Why or why not?