Question

1A) The manager of an assembly process wants to determine whether or not the number of defective articles manufactured depends on the day of the week the articles are produced. She collected the following information. Is there sufficient evidence to reject the hypothesis that the number of defective articles is independent of the day of the week on which they are produced? Use α = 0.05.

Day of Week	M	Tu	W	Th	F
Nondefective	90	93	86	91	88
Defective	6	8	3	14	14

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(b) Find the p-value. (Give your answer bounds exactly.)
< p <

1B) Skittles Original Fruit bite-size candies are multicolored candies in a bag, and you can "Taste the Rainbow" with their five colors and flavors: green, lime; purple, grape; yellow, lemon; orange, orange; and red, strawberry. Unlike some of the other multicolored candies available, Skittles claims that their five colors are equally likely. In an attempt to reject this claim, a 4-oz bag of Skittles was purchased and the colors counted. Does this sample contradict Skittle's claim at the .05 level?

Red	Orange	Yellow	Green	Purple
16	24	25	30	27

(a) Find the test statistic. (Give your answer correct to two decimal places.)


(b) Find the p-value. (Give your answer bounds exactly.)
< p <

Answer 1

Solution:

Question 1A)

We have to test if there is sufficient evidence to reject the hypothesis that the number of defective articles is independent of the day of the week on which they are produced.

Level of significance =

Hypothesis of the study are:

H0: the number of defective articles is independent of the day of the week on which they are produced.

Vs

H1: the number of defective articles is dependent of the day of the week on which they are produced.

Part a) Find the test statistic.

We use Chi-square test of independence.

where

O_ij = Observed frequencies for i^th row and j^th column

E_ij = Expected frequencies for i^th row and j^th column

Day of Week	Mon	Tue	Wed	Thu	Fri	Row Totals
Nondefective	90	93	86	91	88	R1 =448
Defective	6	8	3	14	14	R2 =45
Column Totals	C1 = 96	C2 =101	C3 =89	C4 =105	C5 =102	N = 493

Thus

Thus we get:

Oij	Eij	Oij^2/Eij
90	87.237	92.850
93	91.781	94.235
86	80.876	91.448
91	95.416	86.789
88	92.690	83.548
6	8.763	4.108
8	9.219	6.942
3	8.124	1.108
14	9.584	20.450
14	9.310	21.052
N = 493

Thus

Part b) Find the p-value. (Give your answer bounds exactly.)

df = ( m-1) X ( n-1) = ( 5-1)X(2-1) = 4 X 1 = 4

Look in Chi-square table for df = 4 row and find the interval in which fall and then find corresponding right tail area interval.

fall between 9.488 and 11.143

and its right tail area is between 0.050 and 0.025

that is: 0.025 < p < 0.050

Since p-value < 0.05 level of significance , we reject H0 and thus there is sufficient evidence to reject the hypothesis that the number of defective articles is independent of the day of the week on which they are produced.

That is: the number of defective articles is dependent of the day of the week on which they are produced.