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4.7.1. Consider Example 4.7.2. Suppose the observed frequencies of A₁,..., A4 are 20, 30, 92, and 105, respectively. Modify the R code given in the example to calculate the test for these new frequencies. Report the p-value.

4.7.1. Consider Example 4.7.2. Suppose the observed frequencies of A₁,..., A4 are 20, 30, 92, and 105, respectively. Modify the R code given in the example to calculate the test for these new frequencies. Report the p-value.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 42PFA
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Please skip the part where you are asked to use or modify R codes.
= Example 4.7.2. A point is to be selected from the unit interval {x : 0 < x < 1} by a random process. Let A₁ {x: 0 < x≤ }, A₂ = {x : } < x ≤ ½}, A3 = {x : ½ < x ≤ ³}, and A4 = {x : ³ < x < 1}. Let the probabilities pi, i = 1, 2, 3, 4, assigned to these sets under the hypothesis be determined by the pdf 2x, 0 < x < 1, zero elsewhere. Then these probabilities are, respectively, = 286 P10 = 1/4 ² 3 2x dx = 16, P20 = 16' P30 = 5 16' of Q3 = (Xi - npio)²/(npio) is (6-5)² (18 - 15)² 15 + 5 P40 = Thus the hypothesis to be tested is that p1, P2, P3, and p4 = 1- P1 P2 - p3 have the preceding values in a multinomial distribution with k = 4. This hypothesis is to be tested at an approximate 0.025 significance level by repeating the random experiment n = 80 independent times under the same conditions. Here the npio for i = 1, 2, 3, 4, are, respectively, 5, 15, 25, and 35. Suppose the observed frequencies of A1, A2, A3, and A4 are 6, 18, 20, and 36, respectively. Then the observed value 7 16. Some Elementary Statistical Inferences (20 - 25)² (36 - 35)² 64 + + 25 35 35 - 1.83. The following R segment calculates the test and p-value: x=c (6, 18, 20,36); ps-c (1,3,5,7)/16; chisq.test(x, p-ps) X-squared 1.8286, df = 3, p-value = 0.6087 Hence, we fail to reject Ho at level 0.0250.
Transcribed Image Text:= Example 4.7.2. A point is to be selected from the unit interval {x : 0 < x < 1} by a random process. Let A₁ {x: 0 < x≤ }, A₂ = {x : } < x ≤ ½}, A3 = {x : ½ < x ≤ ³}, and A4 = {x : ³ < x < 1}. Let the probabilities pi, i = 1, 2, 3, 4, assigned to these sets under the hypothesis be determined by the pdf 2x, 0 < x < 1, zero elsewhere. Then these probabilities are, respectively, = 286 P10 = 1/4 ² 3 2x dx = 16, P20 = 16' P30 = 5 16' of Q3 = (Xi - npio)²/(npio) is (6-5)² (18 - 15)² 15 + 5 P40 = Thus the hypothesis to be tested is that p1, P2, P3, and p4 = 1- P1 P2 - p3 have the preceding values in a multinomial distribution with k = 4. This hypothesis is to be tested at an approximate 0.025 significance level by repeating the random experiment n = 80 independent times under the same conditions. Here the npio for i = 1, 2, 3, 4, are, respectively, 5, 15, 25, and 35. Suppose the observed frequencies of A1, A2, A3, and A4 are 6, 18, 20, and 36, respectively. Then the observed value 7 16. Some Elementary Statistical Inferences (20 - 25)² (36 - 35)² 64 + + 25 35 35 - 1.83. The following R segment calculates the test and p-value: x=c (6, 18, 20,36); ps-c (1,3,5,7)/16; chisq.test(x, p-ps) X-squared 1.8286, df = 3, p-value = 0.6087 Hence, we fail to reject Ho at level 0.0250.
4.7.1. Consider Example 4.7.2. Suppose the observed frequencies of A₁,..., A4 are 20, 30, 92, and 105, respectively. Modify the R code given in the example to calculate the test for these new frequencies. Report the p-value.
Transcribed Image Text:4.7.1. Consider Example 4.7.2. Suppose the observed frequencies of A₁,..., A4 are 20, 30, 92, and 105, respectively. Modify the R code given in the example to calculate the test for these new frequencies. Report the p-value.
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Follow-up Question

DEGREES OF FREEDOM=n-1=3

but n=247 right?

also how did you did significant level = .025

did you use any table or any other sources ?

how x^2 3,0.025= 9.348? any table or formula?

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Follow-up Question

how did you get (o-E)^2/E=10.23

 (247-247)^2/247=0

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