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Conduct the hypothesis test and provide | Ch 11.2 - 11 BSC

Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola ISBN: 9780321836960 18

Solution for problem 11 BSC Chapter 11.2

Elementary Statistics | 12th Edition

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Elementary Statistics | 12th Edition | ISBN: 9780321836960 | Authors: Mario F. Triola

Elementary Statistics | 12th Edition

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Problem 11 BSC

Problem  11BSC

Conduct the hypothesis test and provide the test statistic, critical value, and/or P-value, and state the conclusion.

Loaded Die The author drilled a hole in a die and filled it with a lead weight, then proceeded to roll it 200 times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively: 27, 31, 42, 40, 28, 32. Use a 0.05 significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?

Step-by-Step Solution:

Answer:

Step 1 of 2</p>

The expected values for each category, Ei , could be determined. With these observed and expected numbers of cases, the hypotheses can be written as

H0 : O  =    E

H1 : O  E

Use a 0.05 significance level

SL. No.

O

p = 1/6

E = np

(O - E )2

(O - E)2/E

1

27

0.166667

33.33333

40.11111

1.203333

2

31

0.166667

33.33333

5.444444

0.163333

3

42

0.166667

33.33333

75.11111

2.253333

4

40

0.166667

33.33333

44.44444

1.333333

5

28

0.166667

33.33333

28.44444

0.853333

6

32

0.166667

33.33333

1.777778

0.053333

Sum

200

1

200

195.3333

5.86

The first step in conducting the significance test is to compute the expected frequency for each outcome given that the null hypothesis is true. For example, the expected frequency of a "1" is 6 since the probability of a "1" coming up is 1/6 and there were a total of 200.

Expected frequency (E) = np

                                       = 200(1/6)

                                       = 33.33

The calculation continues as follows. Letting E be the expected frequency of an outcome and O be the observed frequency of that outcome.

Step 2 of 2

Chapter 11.2, Problem 11 BSC is Solved
Textbook: Elementary Statistics
Edition: 12
Author: Mario F. Triola
ISBN: 9780321836960

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Conduct the hypothesis test and provide | Ch 11.2 - 11 BSC

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