**Evidence and Perceptions of Tattoos**Research suggests that individuals with visible tattoos may be viewed more negatively than those without (Resenhoeft, Villa, & Wiseman, 2008). In a related study, a researcher evaluated perceptions of attractiveness using a color photograph of a woman without tattoos. The photograph was rated on a 7-point scale, receiving an average score (µ) of 4.9, with a normal distribution and a standard deviation (σ) of 0.84. The researcher then altered the photograph, adding a butterfly tattoo on the woman’s left arm. This modified image was shown to 16 students from a community college. Using the same scale, the students rated the tattooed image, resulting in an average score (M) of 4.2.a. **Purpose**: Assess whether there is a significant difference in perceived attractiveness when the woman has a tattoo, using a two-tailed test with an alpha level (α) of 0.05.b. **Cohen’s d Calculation**: Determine the effect size to gauge the magnitude of potential differences.c. **Research Report Description**: Summarize the findings, including the hypothesis test results and effect size measurement, as would be presented in a formal research setting.

Hypothesized Mean, μ0 = 4.9 Population standard deviation, σ = 0.84 Sample size , n =16 Sample mean, x¯ = 4.2 We have to use a two-tailed test a) Null and Alternative Hypotheses : H0:μ=4.9Ha:μ≠4.9 (There is a significant difference in rated attractiveness when women appeared to have tattoos) Decision Rule : Significance level = α=0.05\alpha = 0.05 Critical value =zc=1.96z_c = 1.96 Rejection region= R={z:∣z∣>1.96}R = \{z: |z| > 1.96\} Reject H0 : if R={z:∣z∣>1.96}R = \{z: |z| > 1.96\} Test Statistics : z=Xˉ−μ0σ/n=4.2−4.90.84/16=−3.333 \begin{array}{ccl} z & = & \displaystyle \frac{\bar X - \mu_0}{\sigma/\sqrt{n}} \\\\ \\\\ & = & \displaystyle \frac{ 4.2 - 4.9}{ 0.84/\sqrt{ 16}} \\\\ \\\\ & = & -3.333 \end{array} Decision : We noticed that ∣z∣=3.333>zc=1.96|z| = 3.333 > z_c = 1.96 Hence null hypothesis is rejected Conclusion : There is enough evidence to claim that There is a significant difference in rated attractiveness when women appeared to have tattoos , at the α=0.05\alpha = 0.05 significance level b) The formula for Cohen's d effect size : Cohen's d = (Sample Mean - µpopulation) ⁄ σ We have : Hypothesized Mean, μ0 = 4.9 Population standard deviation, σ = 0.84 Sample mean, x = 4.2 Cohen's d = (4.2 - 4.9) ⁄ 0.84 = 0.833 c) There is enough evidence to claim that There is a significant difference in rated attractiveness when women appeared to have tattoos , at the α=0.05\alpha = 0.05 significance level According to Cohen's guidelines, d = 0.833 represents a Large effect - mean difference is 0.8 standard deviation (there is s significance difference)