An article reported the following frequencies with which ethnic characters appeared in recorded commercials that aired on Philadelphia television stations.Ethnicity:Frequency:AfricanAmerican59USE SALTAsian11Caucasian HispanicO Ho: P₁ = P₂ = P3 P4 = 0.250H₂: at least one p; # 0.25330In a recent census, the proportions for these four ethnic groups are 0.177, 0.030, 0.734, and 0.059, respectively. Does the data suggest that the proportions in commercials are different from the census proportions? Carry out test of appropriate hypotheses using a significance level of 0.01. (LetP₁, P₂, P3, and P4 be the population proportions of the four ethnic groups (African American, Asian, Caucasian, and Hispanic respectively) appearing in commercials on Philadelphia television stations.)State the appropriate hypotheses.O Ho: P₁ = 0.145, P₂ = 0.027, P = 0.809, P4 = 0.020H₂: at least one p₁ # PioO Ho: P₁ = 0.177, P₂ = 0.030, P3 = 0.734, P4 = 0.059H₂: at least one p; # PioO Ho: P₁0.059, P₂ = 0.011, P3 0.330, P4 = 0.008H₂: at least one p, * PioWhat can be said about the P-value for the test?O P-value < 0.005O 0.005 < P-value < 0.01O 0.01 < P-value < 0.025O 0.025 < P-value < 0.05O 0.05 < P-value < 0.10O P-value > 0.108Calculate the test statistic. (Round your answer to two decimal places.)x² =State the conclusion in the problem context.O Fail to reject Ho. There is enough evidence to conclude that at least one of the racial proportions in commercials is a match to the census proportions.O Reject Ho. There is enough evidence to conclude that at least one of the racial proportions in commercials is not a match to the census proportions.O Reject Ho. There is enough evidence to conclude that none of the racial proportions in commercials is a match to the census proportions.O Fail to reject Ho. There is enough evidence to conclude that all of the racial proportions in commercials are a match to the census proportions.

Solution: Given information : k= 4 categories n= 59+11+330+8= 408 Sample size

n article reported the following frequencies with which ethnic characters appeared in recorded commercials that aired on Philadelphia television stations. African American Ethnicity: Frequency: 59 USE SALT Asian Caucasian Hispanic a recent census, the proportions for these four ethnic groups are 0.177, 0.030, 0.734, and 0.059, respectively. Does the data suggest that the proportions in commercials are different from the census proportions? Carry out a test of appropriate hypotheses using a significance level of 0.01. (Le PP₂, and p be the population proportions of the four ethnic groups (African American, Asian, Caucasian, and Hispanic respectively) appearing in commercials on Philadelphia television stations.) tate the appropriate hypotheses. Ho: P₂ -0.145, P₂ -0.027, p=0.809, P4 -0.020 H.: at least one p, P Ho: P₁0.177, P₂-0.030, P₂-0.734, P4 -0.059 H.: at least one p, P O Ho: Pg P₂P-P-0.250 H.: at least one p, 0.25 330 O Ho: P₂ -0.059, P₂-0.011, P₂-0.330, P-0.008 H₁: at least one p, Po What can be said about the P-value for the test? O P-value < 0.005 O 0.005 < P-value < 0.01 O 0.01 < P-value < 0.025 alculate the test statistic. (Round your answer to two decimal places.) 2-[ O 0.025 < P-value < 0.05 O 0.05 < P-value < 0.10 OP-value > 0.10 8 tate the conclusion in the problem context. O Fail to reject H. There is enough evidence to conclude that at least one of the racial proportions in commercials is a match to the census proportions.

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 4BGP