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Name: Conduct the hypothesis test and provide the test statistic and the cri
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Description: Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion. A company claims that its packages of 100 candies are distributed with the following color percentages:12% red, 21% orange, 16% yellow,

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 5E: List the sample space of each experiment. Rolling one die and tossing one coin

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Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion.

A company claims that its packages of 100 candies are distributed with the following color percentages:12% red, 21% orange, 16% yellow, 11% brown,

23% blue, and 17% green. Use the given sample data to test the claim that the color distribution is as claimed. Use a 0.01 significance level.

Candy Counts

Color

Number in Package

Red

Orange

Yellow

Brown

Blue

Green

The test statistic is

(Round to two decimal places as needed.)

The critical value is

(Round to two decimal places as needed.)

State the conclusion

________H0. There______sufficient evidence to warrant rejection of the claim that the color distribution is as claimed.

Expert Solution

Step 1

The null and alternative hypothesis are stated as,

Null hypothesis:

$H_{0} :$ The distributions are the same.

Alternative hypothesis:

$H_{1} :$ The distributions are different.

The expected values are,

Color	Number in package	Percent	Expected frequency
Red	13	12%	$100 \times 0.12 = 12$
Orange	25	21%	$100 \times 0.21 = 21$
Yellow	10	16%	$100 \times 0.16 = 16$
Brown	6	11%	$100 \times 0.11 = 11$
Blue	27	23%	$100 \times 0.23 = 23$
Green	19	17%	$100 \times 0.17 = 17$

The test statistic is,

$\begin{array}{rcl} χ^{2} & = & \sum_{} \frac{{(O b s e r v e d - E x p e c t e d)}^{2}}{E x p e c t e d} \\ = & \frac{{(13 - 12)}^{2}}{12} + \frac{{(25 - 21)}^{2}}{21} + \frac{{(10 - 16)}^{2}}{16} + \frac{{(6 - 11)}^{2}}{11} + \frac{{(27 - 23)}^{2}}{23} + \frac{{(19 - 17)}^{2}}{17} \\ = & 0.08 + 0.76 + 2.25 + 2.27 + 0.70 + 0.23 \\ = & 6.29 \end{array}$

Thus, the test statistic is 6.29.

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The test statistic is ​(Round to two decimal places as​ needed.) The critical value is ​(Round to two decimal places as​ needed.) State the conclusion ________H0. There______sufficient evidence to warrant rejection of the claim that the color distribution is as claimed.

The test statistic is (Round to two decimal places as needed.) The critical value is (Round to two decimal places as needed.) State the conclusion __H0. Theresufficient evidence to warrant rejection of the claim that the color distribution is as claimed.