Explanation Given info: The New York Time Statement is “mathematicians are pretty sure that the digits of π are indistinguishable from any random sequence.” The data shows that the first 25 decimal places of π . The odd number is denoted by “O” and even number is denoted by “E”. The level of significance is 0.05. Calculation: From the given sequence the odd numbers are 1, 1, 5, 9, 5, 3, 5, 9, 7, 9, 3, 3, 3 and 3. That is, n 1 = 14 . The even numbers are 4, 2, 6, 8, 2, 8, 4, 6, 2, 6 and 4. That is, n 2 = 11 . The hypotheses are given below: Null hypothesis: H 0 : The sequence of digits is random. Alternative hypothesis: H 1 : The sequence of digits is not random. Value of G: Let G be the number of runs in the sequence. A run is the sequence of the same observations. Then, the runs are calculated as follows: Run 1 = { O } Run 2 = { E } Run 3 = { O, O, O } Run 4 = { E, E } Run 5 = { O, O, O } Run 6 = { E

MyLab Statistics with Pearson eText -- Standalone Access Card -- for Elementary Statistics

13th Edition

ISBN: 9780134748535

Author: Mario F. Triola

Publisher: PEARSON

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Chapter 13.7, Problem 6BSC

To determine

To test: The randomness in the way that odd and even digits occur in the sequence.

To check: Whether the statement from the New York Times appears to be accurate or not.

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Chapter 13.7, Problem 5BSC

Chapter 13.7, Problem 7BSC

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Using the Runs Test for Randomness. In Exercises 5–10, use the runs test with a significance level of α=0.05. (All data are listed in order by row.) Odd and Even Digits in Pi A New York Times article about the calculation of decimal places of π noted that “mathematicians are pretty sure that the digits of π are indistinguishable from any random sequence.” Given below are the first 25 decimal places of π. Test for randomness in the way that odd (O) and even (E) digits occur in the sequence. Based on the result, does the statement from the New York Times appear to be accurate?

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Chapter 13 Solutions

MyLab Statistics with Pearson eText -- Standalone Access Card -- for Elementary Statistics

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To test: The randomness in the way that odd and even digits occur in the sequence. To check: Whether the statement from the New York Times appears to be accurate or not.

Solution Summary: The author explains the New York Times' statement that odd and even digits are indistinguishable from any random sequence.