There is some evidence indicating that people with visible tattoos are viewed mo

Question

There is some evidence indicating that people with visible tattoos are viewed more negatively than people without visible tattoos (Resenhoeft, Villa, & Wiseman, 2008). In a similar study, a researcher first obtained overall ratings of attractiveness for a woman with no tattoos shown in a color photograph. On a 7-point scale, the woman received an average rating of mu = 4.9, and the distribution of ratings was normal with a standard deviation of sigma = 0.84. The researcher then modified the photo by adding a tattoo of a butterfly on the woman's left arm. The modified photo was then shown to a sample of n = 16 students at a local community college and the students used the same 7-point scale to rate the attractiveness of the woman. The average score for the photo with the tattoo was M = 4.2. Do the data indicate a significant difference in rated attractiveness when the woman appeared to have a tattoo? Use a two-tailed test with alpha = .05. Compute Cohen's d to measure the size of the effect. Write a sentence describing the outcome of the hypothesis test and the measure of effect size as it would appear in a research report.

Explanation / Answer

Solution:

We have a population with both mean and standard deviation, = 4.9, = 0.84. Then we have one sample, n = 16, with a mean of M = 4.2.
a) Test hypotheses:
H0: = 4.9
H1: 4.9
= 0.05
z = (M-)/standard error = (M-)/(/n)
= (4.2 - 4.9)/(0.84/16)
= (4.2 - 4.9)/0.21 = (-0.7)/0.21 = -3.333... ~ -3.33

Compare t values and decide whether to reject or fail to reject the null. z-observed = -3.33 < -1.96 = z-critical, so we reject the null Hypothesis.

b) Cohen's d = ((with treatment) - (without treatment))/
mean as our sample, so we get mu(with Tx) = 4.2 and mu(w/o Tx) = 4.9 and the given sigma was 0.84.
Cohen's d = (4.2-4.9)/0.84 = (-0.7)/0.84 = -0.8333... ~ -0.83

c) We can conclude that the data indicate a significance difference in rated attractiveness when the women appeared to have a tattoo.

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