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Get Full Access to Elementary Statistics - 12 Edition - Chapter 11.2 - Problem 11 bsc
Get Full Access to Elementary Statistics - 12 Edition - Chapter 11.2 - Problem 11 bsc

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# Conduct the hypothesis test and provide | Ch 11.2 - 11 BSC ISBN: 9780321836960 18

## Solution for problem 11 BSC Chapter 11.2

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:

Step 1 of 2

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

##### ISBN: 9780321836960

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