Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter5: A Survey Of Other Common Functions
Section5.3: Modeling Data With Power Functions
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Minority Models - Negative stereotypical depiction of minorities or their exclusion from advertisements in mainstream media has been found to have
harmful social effects. Researchers are interested in answering the following question:
Is the proportion of magazine advertisements portraying each racial group different from its proportion of the U.S. population?
The observed data in the table below is consistent with data collected from an analysis of magazine advertisements from 1993 and 1994. The table
summarizes the frequency of the appearance of models in a total of 1527 advertisements.
The population distribution values were taken from the 1990 census data.
African
Asian
Hispanic
White
Americans
Americans
Americans
Americans
1990 Census data (%)
12.1%
3.3%
9.0%
75.6%
Observed Data
151
74
80
1222
Round all calculated values to 4 decimal places where appropriate.
1. Select the phrases to complete the null and alternative hypotheses for this research situation.
Ho: The proportion of magazine advertisements portraying each racial group is the same as
v its proportion of the U.S. population.
HA: The proportion of magazine advertisements portraying each racial group is different from v its proportion of the U.S. population.
2. What type of test should the researchers use?
O A. t-test for a sample mean
B. t-test for the slope of the regression line
O C. x² goodness of fit test
OD. x2 test of independence
O E. Z-test for one population proportion
3. Which of the following conditions must be met for the hypothesis test to be valid? Select all that apply.
OA. There must be at least 10 "success" and 10 "failure" observations.
B. There must be an expected count of at least 5 for each level of the categorical variable.
C. Each case in the table must be independent of all other cases.
D. There must be at least 3 levels of the categorical variable.
E. The sample size must be at least 30 or the population data must be normally distributed.
Transcribed Image Text:Minority Models - Negative stereotypical depiction of minorities or their exclusion from advertisements in mainstream media has been found to have harmful social effects. Researchers are interested in answering the following question: Is the proportion of magazine advertisements portraying each racial group different from its proportion of the U.S. population? The observed data in the table below is consistent with data collected from an analysis of magazine advertisements from 1993 and 1994. The table summarizes the frequency of the appearance of models in a total of 1527 advertisements. The population distribution values were taken from the 1990 census data. African Asian Hispanic White Americans Americans Americans Americans 1990 Census data (%) 12.1% 3.3% 9.0% 75.6% Observed Data 151 74 80 1222 Round all calculated values to 4 decimal places where appropriate. 1. Select the phrases to complete the null and alternative hypotheses for this research situation. Ho: The proportion of magazine advertisements portraying each racial group is the same as v its proportion of the U.S. population. HA: The proportion of magazine advertisements portraying each racial group is different from v its proportion of the U.S. population. 2. What type of test should the researchers use? O A. t-test for a sample mean B. t-test for the slope of the regression line O C. x² goodness of fit test OD. x2 test of independence O E. Z-test for one population proportion 3. Which of the following conditions must be met for the hypothesis test to be valid? Select all that apply. OA. There must be at least 10 "success" and 10 "failure" observations. B. There must be an expected count of at least 5 for each level of the categorical variable. C. Each case in the table must be independent of all other cases. D. There must be at least 3 levels of the categorical variable. E. The sample size must be at least 30 or the population data must be normally distributed.
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