Question

In: Statistics and Probability

A candy company says that the colors of its candies are 15% yellow, 14% red, 19%...

A candy company says that the colors of its candies are 15% yellow, 14% red, 19% orange, 25% blue, 15% green and 12% brown. In a randomly selected bag of the candies, there were 26 yellow, 24 red, 11 orange, 10 blue, 10 green, 20 brown. Is this sample consistent with the company's advertised proportions? Test an appropriate hypothesis and state your conclusion. Complete parts a through g below. Fill in blanks

a) If the company's candies are packaged in the advertised proportions, how many of each color should have been expected in the bag of candies?

(blank)

Yellow

(blank)

Red

(blank)

Orange

(blank)

Blue

(blank)

Green

(blank)

Brown

(Type integers or decimals rounded to two decimal places as needed.)

b) To see if the bag was unusual, should the test be for goodness-of-fit, homogeneity, or independence?

Choose the correct answer below.

A. Goodness-of-fit

B. Homogeneity

C. Independence

c) State the hypothesis

d) Check the conditions.

Select all assumptions and conditions below that are satisfied by the data.

A. Expected cell frequency condition

B. Counted data condition

C. Independence assumption

D. Randomization condition

e) How many degrees of freedom are there?

There are (blank) degrees of freedom. (Simplify your answer.)

f) Find chi squaredχ2 and the P-value.

chi squaredχ2 =

(Round to four decimal places as needed.)

P=

(Round to four decimal places as needed.)

g) State a conclusion. Assume that 0.05 is a reasonable significance level.

(blank) the hypothesis. There is (blank) evidence that the distribution of colors is not the distribution specified by the company.

Expert Solution

a)since expected frequency =Np

Category	Yellow	red	Orange	Blue	Green	Brown
Expected	15.15	14.14	19.19	25.25	15.15	12.12

b)
A. Goodness-of-fit

c)

All are satisfied

e)

degree of freedom =categories-1=

5

f)

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
Category	frequency(p)	O_i	E_i=total*p	R²_i=(O_i-E_i)/√E_i	R²_i=(O_i-E_i)²/E_i
Yellow	0.1500	26	15.15	2.7876	7.7705
red	0.1400	24	14.14	2.6221	6.8755
Orange	0.1900	11	19.19	-1.8696	3.4954
Blue	0.2500	10	25.25	-3.0349	9.2104
Green	0.1500	10	15.15	-1.3231	1.7507
Brown	0.1200	20	12.12	2.2635	5.1233
total	1.00	101	101		34.2257

test statistic X²=		34.2257

p value =

0.0000

from excel: chidist(34.226,5)

reject the null hypothesis

There is sufficient evidence that the distribution of colors is not the distribution specified by the company.

orchestra answered 1 year ago

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