Question

The authors of a paper studied 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 are given in the table. Assume that this sample is representative of smoking movie characters. Do these 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	130
Female	85	13	49

State the appropriate null and alternative hypotheses.

H₀: The proportions falling into the character type categories are not the same for the two sexes.
H_a: The proportions falling into the character type categories are the same for the two sexes. H₀: There is an association between sex and character type.
H_a: There is no association between sex and character type.     H₀: The proportions falling into the character type categories are the same for the two sexes.
H_a: The proportions falling into the character type categories are not the same for the two sexes. H₀: There is no association between sex and character type.
H_a: There is an association between sex and character type.

Find the test statistic and P-value. (Use technology. Round your test statistic to three decimal places and your P-value to four decimal places.)

X² = P-value =

State the conclusion in the problem context.

Fail to reject H₀. There is not convincing evidence to conclude that there is an association between sex and character type for movie characters who smoke. Reject H₀. There is convincing evidence to conclude that the proportions falling into the character type categories are not the same for the two sexes.     Fail to reject H₀. There is not convincing evidence to conclude that the proportions falling into the character type categories are not the same for the two sexes. Reject H₀. There is convincing evidence to conclude that there is an association between sex and character type for movie characters who smoke.

Answer 1

The statistical software output for this problem is:

Hence,

Hypotheses: H₀: There is no association between sex and character type.
H_a: There is an association between sex and character type.

Test statistic = 12.652

p - Value = 0.0018

Conclusion: Option D is correct.