Question

Q1- In the Super-Mega lottery there are 50 numbers (1 to 50), a player chooses ten different numbers and hopes that these get drawn. If the player's numbers get drawn, he/she wins an obscene amount of money. The table below displays the frequency with which classes of numbers are chosen (not drawn). These numbers came from a sample of 194 chosen numbers.

	Chosen Numbers (n=194)
	1 to 10	11 to 20	21 to 30	31 to 40	41 to 50
Count	46	39	32	24	53

Test the claim that chosen numbers are not evenly distributed across the five classes. Test this claim at the 0.05 significance level.

(a) Find the test statistic.=

(b) Find the critical value.=

Q2-

The number of men and women among professors in Math, Physics, Chemistry, Linguistics, and English departments from a SRS of small colleges were counted, and the results are shown in the table below.

Dept.	Math	Physics	Chemistry	Linguistics	English
Men	70	89	34	24	42
Women	6	5	8	14	17

Test the claim that the gender of a professor is independent of the department. Use the significance level α=0.01

(a) The test statistic is χ2=

(b) The critical value is χ2=

Answer 1