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Do the successive digits in the decimal expansion of a behave as though they were selected from a random number table (or came from a computer's random number generator)? (a) Let po denote the long run proportion of digits in the expansion that equal 0, and define p,, ..., Pg analogously. What hypotheses about these proportions should be tested? O Ho: P = P2 = ...- Pg = 0.10 H: all p, # 0.10 O Ho: P1 = P2 = ... = Pg = 0.10 H: at least one p, + 0.10 O Ho: Po = P1 = ... = Pg = 0.10 H: all p, = 0.10 O Ho: Po = P1 = ...= Pg = 0.10 H: at least one p, + 0.10 What is df for the chi-squared test? df = (b) H, of part (a) would not be rejected for the nonrandom sequence 012...901 . . . 901.... Consider nonoverlapping groups of two digits, and let p; denote the long run proportion of groups for which the first digit is i and the second digit is j. What hypotheses about these proportions should be tested? O Ho: P= 0.01 for i and j = 1,2,...,9 H: at least one p* 0.01 O Ho: P = 0.10 for i and j = 0,1,2,..,9 H: at least one p* 0.10 O Ho: P = 0.01 for i and j = 0,1,2,...,9 H: at least one p* 0.01 O Ho: Pij = 0.10 for i and j = 1,2,...,9 H: at least one P* 0.10 What is df for the chi-squared test?

Do the successive digits in the decimal expansion of a behave as though they were selected from a random number table (or came from a computer's random number generator)? (a) Let po denote the long run proportion of digits in the expansion that equal 0, and define p,, ..., Pg analogously. What hypotheses about these proportions should be tested? O Ho: P = P2 = ...- Pg = 0.10 H: all p, # 0.10 O Ho: P1 = P2 = ... = Pg = 0.10 H: at least one p, + 0.10 O Ho: Po = P1 = ... = Pg = 0.10 H: all p, = 0.10 O Ho: Po = P1 = ...= Pg = 0.10 H: at least one p, + 0.10 What is df for the chi-squared test? df = (b) H, of part (a) would not be rejected for the nonrandom sequence 012...901 . . . 901.... Consider nonoverlapping groups of two digits, and let p; denote the long run proportion of groups for which the first digit is i and the second digit is j. What hypotheses about these proportions should be tested? O Ho: P= 0.01 for i and j = 1,2,...,9 H: at least one p* 0.01 O Ho: P = 0.10 for i and j = 0,1,2,..,9 H: at least one p* 0.10 O Ho: P = 0.01 for i and j = 0,1,2,...,9 H: at least one p* 0.01 O Ho: Pij = 0.10 for i and j = 1,2,...,9 H: at least one P* 0.10 What is df for the chi-squared test?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Do the successive digits in the decimal expansion of n behave as though they were selected from a random number table (or came from a computer's random number generator)? (a) Let po denote the long run proportion of digits in the expansion that equal 0, and define p,, ..., Pg analogously. What hypotheses about these proportions should be tested? O Ho: P1 = P2 = . .. = Pg = 0.10 H: all P; + 0.10 O Ho: P, = P2 = = P. = 0.10 H: at least one p; + 0.10 O Ho: Po = P, = ... = P, = 0.10 H: all p; + 0.10 O Ho: Po = P, = ... = P, = 0.10 H: at least one p; + 0.10 What is df for the chi-squared test? df = (b) H, of part (a) would not be rejected for the nonrandom sequence 012... 901 ... 901.... Consider nonoverlapping groups of two digits, and let p;; denote the long run proportion of groups for which the first digit is i and the second digit is j. What hypotheses about these proportions should be tested? O Ho: Pij = 0.01 for i and j = 1,2,...,9 H: at least one Pi * 0.01 Hoi Pij = 0.10 for i and j = 0,1,2,...,9 H: at least one p; + 0.10 Ho: Pij = 0.01 for i and j = 0,1,2,...,9 Ha: at least one p; + 0.01 O Ho: Pij = 0.10 for i and j = 1,2,...,9 H: at least one Pij + 0.10 What is df for the chi-squared test?
Transcribed Image Text:Do the successive digits in the decimal expansion of n behave as though they were selected from a random number table (or came from a computer's random number generator)? (a) Let po denote the long run proportion of digits in the expansion that equal 0, and define p,, ..., Pg analogously. What hypotheses about these proportions should be tested? O Ho: P1 = P2 = . .. = Pg = 0.10 H: all P; + 0.10 O Ho: P, = P2 = = P. = 0.10 H: at least one p; + 0.10 O Ho: Po = P, = ... = P, = 0.10 H: all p; + 0.10 O Ho: Po = P, = ... = P, = 0.10 H: at least one p; + 0.10 What is df for the chi-squared test? df = (b) H, of part (a) would not be rejected for the nonrandom sequence 012... 901 ... 901.... Consider nonoverlapping groups of two digits, and let p;; denote the long run proportion of groups for which the first digit is i and the second digit is j. What hypotheses about these proportions should be tested? O Ho: Pij = 0.01 for i and j = 1,2,...,9 H: at least one Pi * 0.01 Hoi Pij = 0.10 for i and j = 0,1,2,...,9 H: at least one p; + 0.10 Ho: Pij = 0.01 for i and j = 0,1,2,...,9 Ha: at least one p; + 0.01 O Ho: Pij = 0.10 for i and j = 1,2,...,9 H: at least one Pij + 0.10 What is df for the chi-squared test?
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