Answered: The test statistic is (Round to two…

Name: Conduct the hypothesis test and provide the test statistic and the cri
Uploaded: 2024-03-20T07:07:00.000Z
Channel: Bartleby
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,

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

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.

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hypothesis Tests and Confidence Intervals for Proportions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Similar questions