Question

A gambler thinks a die may be loaded, that is, that the six numbers are not equally likely. To test his suspicion, he rolled a die 150 times and obtained the data (1 - 23, 2- 26, 3- 23, 4- 21, 5- 31, 6- 26). Do the data provide sufficient evidence to conclude that the die is loaded?

Answer 1

here null hypothesis:Ho: p1=p2=p3=p4=p5=p6=1/6

Alternate hypothesis:Ha: at least pi is not equal to 1/6

degree of freedom =categories-1=

5

for 5 df and 0.05 level of signifcance critical region       χ2=

11.070

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	1/6	23	25.000	-0.40	0.160
2	1/6	26	25.000	0.20	0.040
3	1/6	23	25.000	-0.40	0.160
4	1/6	21	25.000	-0.80	0.640
5	1/6	31	25.000	1.20	1.440
6	1/6	26	25.000	0.20	0.040
total	1.000	150	150		2.480

as test statistic is less than critical value we can not reject null hypothesis

we do not have evidence to conclude that die is loaded,