Question

5. (30 points) A food company is developing a new granola bar, and its market analysts are currently working on preliminary studies of the packaging design. To help with a marketing strategy, the company was first interested in whether the appeal of the packaging design for the new product (and hence the appeal of the product itself) was related to a person's gender. There were 100 male and 100 female volunteers available for purposes of evaluation. Both males and females rated the design on a scale of 1 to 10, 1 being “very unappealing" and 10 being "very appealing". The mean rating for males was 7.4 with a standard deviation 1.5. The mean rating for females was 8.0 with a standard deviation 2.0. Assume our samples can be regarded as random samples from the populations of males and females. 1) (10 points) Is there good evidence that the mean rating for the population of males is different from that for the population of females? State the Ho and Ha and carry out an appropriate test statistic. Give the P-value and state your conclusion using significance level a = 0.05. 2) (5 points) Give a 95% confidence interval for the difference in the mean ratings between males and females.

Answer 1

(2 t) + 742 Giden date = 7.4 S = 1.5 n, -100 8 82 2 Se + n=100 .) Ho: Ole = llz Hi all & 2 (2 tailed) -0.6 -74-8 Test Statistics 24 X2 Z 0.25 2 hog SL +2 100 100 n Z: -2.140 P-vake for 2 tailed 0.0164 P- zx P[< < -2:40) = 2 X 0.0082 (from Itable) P=0.0164 p=0.0164 <0.05 Reject Ho Thece is Bufficient evidence to support the claim that the rating for males different from that fa female 2) 15. CI to.o25 = 1.96 the mean Population q the -0.95 x 0.057412 (Fran z tebe) 95% CI + ماته n2 2 (1.4-8) + 1.96 1.5? + 2 100 100 - 0.6 t & a6 x 0.25 5.06 t 0.49 95 la -1.09 el« -0.11