Question

The authors of a paper classified characters who were depicted smoking in movies released between a...

The authors of a paper classified characters who were depicted smoking in movies released between a certain range of years. The smoking characters were classified according to sex and whether the character type was positive, negative, or neutral. The resulting data is given in the accompanying table.

Assume that it is reasonable to consider this sample of smoking movie characters as representative of smoking movie characters. Do the data provide evidence of an association between sex and character type for movie characters who smoke? Use

α = 0.05.

Character Type
Sex Positive Negative Neutral
Male 257 107 132
Female 86 11 50

State the null and alternative hypotheses.

H0: Sex and character type are independent.
Ha: Sex and character type are not independent.

H0: The character type category proportions are not all the same for male and female characters.
Ha: The character type category proportions are the same for male and female characters.  

H0: Sex and character type are not independent.
Ha: Sex and character type are independent.

H0: The character type category proportions are the same for male and female characters.
Ha: The character type category proportions are not all the same for male and female characters.


Calculate the test statistic. (Round your answer to two decimal places.)
χ2 =  

What is the P-value for the test? (Round your answer to four decimal places.)
P-value =  

What can you conclude?

Do not reject H0. There is not enough evidence to conclude that the proportions falling into the character type categories are not all the same for the two gender groups.

Reject H0. There is convincing evidence to conclude that the proportions falling into the character type categories are not all the same for the two gender groups.   

Reject H0. There is convincing evidence to conclude that there is an association between sex and character type for movie characters who smoke.

Do not reject H0. There is not enough evidence to conclude that there is an association between sex and character type for movie characters who smoke.

Homework Answers

Answer #1

H0: Sex and character type are independent.
Ha: Sex and character type are not independent.

===============================================

Tabulated Statistics: Sex, Worksheet columns

Rows: Sex   Columns: Worksheet columns

Positive Negative Neutral All
Male 257 107 132 496
Expected count 264.58 91.02 140.39
Female 86 11 50 147
Expected count 78.42 26.98 41.61
All 343 118 182 643

Cell Contents
      Count
     

Chi-Square Test

Chi-Square DF P-Value
Pearson 15.412 2 0.000

====================================================

P-value = 0.0005

====================================================

Reject H0. There is convincing evidence to conclude that there is an association between sex and character type for movie characters who smoke.

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