An article reported the following frequencies with which ethnic characters appeared in recorded commercials that aired on Philadelphia television stations. African Ethnicity: Asian Caucasian Hispanic American Frequency: 48 11 330 5 In a recent census, the proportions for these four ethnic groups are 0.177, 0.041, 0.734, and 0.048, 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. (Let P P2i P3, 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.)
An article reported the following frequencies with which ethnic characters appeared in recorded commercials that aired on Philadelphia television stations. African Ethnicity: Asian Caucasian Hispanic American Frequency: 48 11 330 5 In a recent census, the proportions for these four ethnic groups are 0.177, 0.041, 0.734, and 0.048, 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. (Let P P2i P3, 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.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:An article reported the following frequencies with which ethnic characters
appeared in recorded commercials that aired on Philadelphia television
stations.
African
Ethnicity:
Asian
Caucasian
Hispanic
American
Frequency:
48
11
330
5
In a recent census, the proportions for these four ethnic groups are 0.177,
0.041, 0.734, and 0.048, 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. (Let
P, Pz. Pz, 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.)
State the appropriate hypotheses.
O Ho: P, = 0.122, p2 = 0.028, p3 = 0.838, p4 = 0.013
H: at least one p; + Pio
Ho: P1 = 0.177, P2 = 0.041, p3 = 0.734, P4 = 0.048
H3: at least one p; + Pio
O Ho: P1 - P2 = P3 = P4 = 0.250
H: at least one p, + 0.25
Pi
O Ho: P, = 0.048, p, - 0.011, p3 = 0.330, p = 0.005
H: at least one p, + Pio
Calculate the test statistic. (Round your answer to two decimal places.)
What can be said about the P-value for the test?
O P-value < 0.005
O 0.005 < P-value < 0.01
0.01 < P-value < 0.025
0.025 < P-value < 0.05
0.05 < P-value < 0.10
O P-value > 0.10
State the conclusion in the problem context.
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.
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 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.
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