Statistics: Informed Decisions Using Data (5th Edition)
Statistics: Informed Decisions Using Data (5th Edition)
5th Edition
ISBN: 9780134133539
Author: Michael Sullivan III
Publisher: PEARSON
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Chapter 12, Problem 1RE
To determine

To test: The claim that is the wheel out of balance.

Expert Solution & Answer
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Answer to Problem 1RE

Solution: There is an inadequate indication to discard the null hypothesis.

Explanation of Solution

Given: The sample size is n=500.

Explanation: To test the hypothesis, the null and alternate hypotheses are defined in the following manner:

H0:The roulette wheel is balanced.H1:The wheel is not in balance.

The observed frequencies Oi are shown in the table below:

Outcome Observed frequency (Oi)
Black 233
Red 237
Green 30
Total 500

The expected frequencies Ei are obtained using the formula

Ei=npi

where n is the number of trials and pi is the probability of success in the ith trial.

In the given problem, n=500.

The expected frequencies Ei corresponding to each outcome are shown below:

Outcome Number of slots npi Expected frequency (Ei)
Black 18 500×1838 236.84
Red 18 500×1838 236.84
Green 2 500×238 26.32
Total 38 500

The test statistic is calculated as follows:

χ02=(OiEi)2EI=(233236.84)2236.84+(237236.84)2236.84+(3026.32)226.32=0.577

where χ02 follows the chi-square distribution with (k1). The critical values are obtained using the Table VIII provided in the book.

k1=31=2

Therefore, the critical values are observed as follows:

χα2=χ0.052=χ0.052=5.991

Therefore, there is an inadequate indication to discard the null hypothesis because the value of test statistic (χ02) is less than the critical value (χ0.052).

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Chapter 12 Solutions

Statistics: Informed Decisions Using Data (5th Edition)

Ch. 12.1 - NW 11. Plain M&Ms According to the manufacturer of...Ch. 12.1 - 12. Peanut M&Ms According to the manufacturer of...Ch. 12.1 - Prob. 13AYUCh. 12.1 - Prob. 14AYUCh. 12.1 - 15. Always Wear a Helmet The National Highway...Ch. 12.1 - 16. Religion in Congress Is the religious make-up...Ch. 12.1 - Prob. 17AYUCh. 12.1 - Prob. 18AYUCh. 12.1 - NW 19. The NHL In his book Outliers, Malcolm...Ch. 12.1 - Prob. 20AYUCh. 12.1 - Prob. 21AYUCh. 12.1 - Prob. 22AYUCh. 12.1 - Prob. 23AYUCh. 12.1 - Prob. 24AYUCh. 12.1 - Prob. 25AYUCh. 12.1 - Prob. 26AYUCh. 12.1 - Prob. 27AYUCh. 12.1 - 28. Putting It Together: Weldon's Dice On February...Ch. 12.1 - Prob. 29AYUCh. 12.1 - Prob. 30AYUCh. 12.1 - 31. Explain why chi-square goodness-of-fit tests...Ch. 12.1 - Prob. 32AYUCh. 12.2 - 1. True or False: The expected frequencies in a...Ch. 12.2 - Prob. 2AYUCh. 12.2 - Prob. 3AYUCh. 12.2 - Prob. 4AYUCh. 12.2 - Prob. 5AYUCh. 12.2 - Prob. 6AYUCh. 12.2 - Prob. 7AYUCh. 12.2 - Prob. 8AYUCh. 12.2 - Prob. 9AYUCh. 12.2 - Prob. 10AYUCh. 12.2 - Prob. 11AYUCh. 12.2 - Prob. 12AYUCh. 12.2 - Prob. 13AYUCh. 12.2 - Prob. 14AYUCh. 12.2 - NW 15. What's in a Word? In a recent survey...Ch. 12.2 - Prob. 16AYUCh. 12.2 - Prob. 17AYUCh. 12.2 - Prob. 18AYUCh. 12.2 - Prob. 19AYUCh. 12.2 - Prob. 20AYUCh. 12.2 - Prob. 21AYUCh. 12.2 - 22. Homeruns Go to...Ch. 12.2 - Prob. 23AYUCh. 12.2 - Prob. 24AYUCh. 12.3 - In Problems 1 and 2, test whether the population...Ch. 12.3 - Prob. 2AYUCh. 12.3 - Prob. 3AYUCh. 12.3 - Prob. 4AYUCh. 12.3 - Prob. 5AYUCh. 12.3 - Prob. 6AYUCh. 12.3 - Prob. 7AYUCh. 12.3 - 8. Children and Childcare The General Social...Ch. 12 - Prob. 1RECh. 12 - Prob. 2RECh. 12 - Prob. 3RECh. 12 - Prob. 4RECh. 12 - Prob. 5RECh. 12 - Prob. 6RECh. 12 - Prob. 1CTCh. 12 - Prob. 2CTCh. 12 - Prob. 3CTCh. 12 - Prob. 4CTCh. 12 - Prob. 5CTCh. 12 - Prob. 6CTCh. 12 - Prob. CS
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