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Daily News reported that the color distribution for plain M&M’s was: 40% brown,

ID: 3232680 • Letter: D

Question

Daily News reported that the color distribution for plain M&M’s was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M’s was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct.

(a) Identify the null hypothesis and the alternative hypothesis.

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

(c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(d) Is there sufficient evidence to support the claim that the published color distribution is correct? Justify your answer.

Color

Brown

Yellow

Orange

Green

Tan

Number

42

18

15

7

18

Color

Brown

Yellow

Orange

Green

Tan

Number

42

18

15

7

18

Explanation / Answer

Answer:

Daily News reported that the color distribution for plain M&M’s was: 40% brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M’s was classified according to color, and the results are listed below. Use a 0.05 significance level to test the claim that the published color distribution is correct.

(a) Identify the null hypothesis and the alternative hypothesis.

Ho: the published color distribution is correct

H1: the published color distribution is not correct

(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

42

40.000

2.000

0.100

18

20.000

-2.000

0.200

15

20.000

-5.000

1.250

7

10.000

-3.000

0.900

18

10.000

8.000

6.400

Total

100

100.000

0.000

8.850

8.85

chi-square

4

df

.0650

p-value

(c) Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit.

P=0.065

Excel function to get p value : =CHISQ.DIST.RT(8.85,4)

(d) Is there sufficient evidence to support the claim that the published color distribution is correct? Justify your answer.

Calculated chi square =8.85,.

P=0.0650 > 0.05 level. Ho is not rejected.

There is no sufficient evidence to reject the claim that the published color distribution is correct.

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

42

40.000

2.000

0.100

18

20.000

-2.000

0.200

15

20.000

-5.000

1.250

7

10.000

-3.000

0.900

18

10.000

8.000

6.400

Total

100

100.000

0.000

8.850

8.85

chi-square

4

df

.0650

p-value