The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts (a) and (b) below. X1 X2 X3 32 41 49 (33.85)(42.31)(45.84)| 16 19 16 Y2 |(14.15)(17.69)(19.16) (a) Compute the value of the chi-square test statistic. X6 = (Round to three decimal places as needed.) (b) Test the hypothesis that X and Y are independent at the a = 0.1 level of significance. O A. Ho: The Y category and X category are independent. : The Y category and X category are dependent. H4: O B. Ho: The Y category and X category have equal proportions. H,: The proportions are not equal. O C. Ho: Hx = Ex and Hy = Ey H4: Hx #Ex or Hy # Ey D. Ho: The Y category and X category are dependent. H,: The Y category and X category are independent. What is the P-value? P-value = (Round to three decimal places as needed.) Should the null hypothesis be rejected? O A. Yes, reject Ho. There is not sufficient evidence at the a = 0.1 level of significance to conclude that X and Y are dependent because the P-value < a. B. No, do not reject Ho. There is sufficient evidence at the a = 0.1 level of significance to conclude that X and Y are dependent because the P-value a. O D. No, do not reject Ho. There is not sufficient evidence at the a = 0.1 level of significance to conclude that X and Y are dependent because the P-value >a.
The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts (a) and (b) below. X1 X2 X3 32 41 49 (33.85)(42.31)(45.84)| 16 19 16 Y2 |(14.15)(17.69)(19.16) (a) Compute the value of the chi-square test statistic. X6 = (Round to three decimal places as needed.) (b) Test the hypothesis that X and Y are independent at the a = 0.1 level of significance. O A. Ho: The Y category and X category are independent. : The Y category and X category are dependent. H4: O B. Ho: The Y category and X category have equal proportions. H,: The proportions are not equal. O C. Ho: Hx = Ex and Hy = Ey H4: Hx #Ex or Hy # Ey D. Ho: The Y category and X category are dependent. H,: The Y category and X category are independent. What is the P-value? P-value = (Round to three decimal places as needed.) Should the null hypothesis be rejected? O A. Yes, reject Ho. There is not sufficient evidence at the a = 0.1 level of significance to conclude that X and Y are dependent because the P-value < a. B. No, do not reject Ho. There is sufficient evidence at the a = 0.1 level of significance to conclude that X and Y are dependent because the P-value a. O D. No, do not reject Ho. There is not sufficient evidence at the a = 0.1 level of significance to conclude that X and Y are dependent because the P-value >a.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 30PPS
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Transcribed Image Text:The table to the right contains observed values and expected values in parentheses for two categorical variables, X and Y, where variable X has three categories and variable Y has two categories. Use the table to complete parts (a) and (b) below.
X1
X2
X3
32
41
49
(33.85)(42.31)(45.84)|
16
19
16
Y2
|(14.15)(17.69)(19.16)
(a) Compute the value of the chi-square test statistic.
X6 = (Round to three decimal places as needed.)
(b) Test the hypothesis that X and Y are independent at the a = 0.1 level of significance.
O A. Ho: The Y category and X category are independent.
: The Y category and X category are dependent.
H4:
O B. Ho: The Y category and X category have equal proportions.
H,: The proportions are not equal.
O C. Ho: Hx = Ex and Hy = Ey
H4: Hx #Ex or
Hy # Ey
D. Ho: The Y category and X category are dependent.
H,: The Y category and X category are independent.
What is the P-value?
P-value =
(Round to three decimal places as needed.)
Should the null hypothesis be rejected?
O A. Yes, reject Ho. There is not sufficient evidence at the a = 0.1 level of significance to conclude that X and Y are dependent because the P-value < a.
B. No, do not reject Ho. There is sufficient evidence at the a = 0.1 level of significance to conclude that X and Y are dependent because the P-value <a.
C. Yes, reject Ho. There is not sufficient evidence at the a = 0.1 level of significance to conclude that X and Y are dependent because the P-value > a.
O D. No, do not reject Ho. There is not sufficient evidence at the a = 0.1 level of significance to conclude that X and Y are dependent because the P-value >a.
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