Question

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.
H_a: Sex and character type are not independent.

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

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

H₀: The character type category proportions are the same for male and female characters.
H_a: 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.

Answer 1

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

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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

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P-value = 0.0005

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