Question 3 (7 parts): 'Purchase intention' is an important metric for new products. When a new product is developed, a sample of potential buyers is shown a prototype or detailed description of the product and asked about their likelihood of buying it. While people may overestimate their likelihood of purchasing a new product, purchase intention has proven to be an effective predictor of new product success. With that in mind, a skin care products company provided a random sample of 500 potential customers with a new formulation of moisturizing cream. After using the cream, participants were interviewed and asked about their intention to purchase it. From the sample of 500, 269 responded that they intend to purchase the new product. that intend to purchase the new product. a. Compute the sample proportion, b. If purchase intention over 50% is a predictor of success for the new product, develop the appropriate hypothesis test to determine whether the sample provides strong evidence that the new product will be successful. Specifically, state the null hypothesis, the alternative hypothesis, and compute the test statistic. Is this a one- tailed test to the left, a one-tailed test to the right, or a two-tailed test? c. What is the p-value for the test statistic computed in (b)? Write the Excel function you used to determine this p-value, including the inputs that you entered in the Excel function (do not give cell references; write in the actual numbers). d. Based on the results from (c), what is your conclusion about the true population purchase intention at a = .05. e. After formulating the new product, the skin care products company created materials to support the product's launch (i.e., new packaging, marketing materials, and communications). A second sample of 300 potential customers were provided with the new product, this time in its new packaging, and were exposed to the new marketing materials and communications. From this second sample of 300, 177 said that they intend to purchase the new product. Now develop the appropriate hypothesis test to determine whether there is strong evidence that purchase intention for the new product with materials to support the product launch (from the second sample), is greater than purchase intention for the new product without these materials (from the first sample). Specifically, state the null hypothesis and the alternative hypothesis. Is this a one-tailed test to the left, a one-tailed test to the right, or a two-tailed test? Compute the pooled sample proportion p (which assumes that the null hypothesis is true). f. Compute the test statistic and the p-value. g. Based on the results from (f), what is your conclusion about purchase intention for the new product, with and without supporting materials, at a = .05.