Question #8 part A & BWith df is a=.05 **Problem 8: Analysis of Cell Phone Design Preferences Among College Students**A communications company developed three new designs for a cell phone. To assess consumer preferences, a sample of 120 college students tried all three phones over one week. Afterward, they selected their preferred design. The distribution of preferences is:- **Design 1**: 54- **Design 2**: 38- **Design 3**: 28**Tasks:**a. Determine if the results show any significant preferences among the three designs.b. Calculate Cohen’s $ w $ to measure the effect size.**Problem 9: Comparison of Preferences Between College Students and Older Adults**Continuing from Problem 8, a researcher hypothesized that college students and older adults may have differing criteria for cell phone design preferences. To test this, the study was repeated with a sample of 60 older adults along with the 60 students. The distribution of preferences is:- **Students**: - Design 1: 27 - Design 2: 20 - Design 3: 13- **Older Adults**: - Design 1: 21 - Design 2: 34 - Design 3: 5**Total Distribution**:- Design 1: 48- Design 2: 54- Design 3: 18This data helps analyze differing preferences based on age demographics for new cell phone designs.

The categorical variable is design. There are 3 designs of data are drawn. The sample size is 120. We have to test whether the preferences among the three designs are different or not. This is Chi-square test for goodness-of-fit.The null and alternative hypotheses are Sample Observed Proportions Expected O-E (O-E)^2/E Design 1 54 0.3333 40 14 4.9 Design 2 38 0.3333 40 -2 0.1 Design 3 28 0.3333 40 -12 3.6 Total 120 120 8.6The value of the test statistic is = 8.60. Df = n-1 = 3-1 = 2. From Chi-square distribution table, the critical value at 2 df and 0.05 level is 5.991. Conclusion: Since X^2(=8.60) > 5.991, then reject the null hypothesis. The results indicate significant preferences among the three designs.The value of Cohen’s w is 0.2677. The size of the effect is medium.