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A food company is developing a new granola bar, and its market analysts are currently working...

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 ¯x1 = 7.4, with a standard deviation s1 = 1.5. The mean rating for females was ¯x2 = 8.0, with a standard deviation s2 = 2.0. Let µ1 and µ2 represent the mean ratings we would observe for the populations of males and females, respectively, and assume our samples can be regarded as samples from these populations. (Hint: this is Case 2: large-sample case.)

(a) Calculate a 90% confidence interval for µ1 − µ2.

(b) Test whether the package design for the new product is related to a person’s gender. i.e. whether there is a difference between the average appealing scores of male and female customers.

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