people without visible tattoos (Resenhoeft, Villa,There is some evidence indicating that people withvisible tattoos are viewed more negatively thanpeople without visible tattoos (Resenhoeft, Villa,& Wiseman, 2008). In a similar study, a researcherfirst obtained overall ratings of attractiveness for awoman with no tattoos shown in a color photographOn a 7-point scale, the woman received an averagerating of u. = 4.9, and the distribution of ratings wanormal with a standard deviation of ơ =researcher then modified the photo by adding a tattoof a butterfly on the woman's left arm. The modifiephoto was then shown to a sample of n =16 stu-dents at a local community college and the studentsused the same 7-pt scale to rate the attractivenessof the woman. The average score for the photo withthe tattoo was M 4,2.a. Do the data indicate a significant difference inrated attractiveness when the woman appeared tohave a tattoo? Use a two-tailed test with a = .05b. Compute Cohen's d to measure the size of theeffect.0.84. Thec. Write a sentence describing the outcome of thehypothesis test and the measure of effect size as

Given : Hypothesized Mean, μ0 = 4.9 Population standard deviation, σ = 0.84 Sample mean , x = 4.2 Null and Alternative Hypotheses : (Two Tailed) H0:μ=4.9Ha:μ≠4.9 \begin{array}{ccl} H_0: \mu & = & 4.9 \\\\ \\\\ H_a: \mu & \ne & 4.9 \end{array} 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 Hence null hypothesis is rejected Conclusion : There is enough evidence to claim that there is a significant difference in rated attractiveness , at the α=0.05\alpha = 0.05 significance level b) Cohen D formula : (Effect Size) Cohen's d = (Meansample - µpopulation) ⁄ σ 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 tattoo , at the α=0.05\alpha = 0.05 significance level Here, d = 0.833 , According to Cohen guidelines it represents a Large effect - mean difference is 0.8 standard deviation