12 May A consumer products firm has rece
A consumer products firm has recently introduced a new brand. The firm would like to estimate the proportion of people in its target market segment who are aware of the new brand. As part of a larger market research study, it was found that in a sample of 125 randomly selected individuals from the target market segment, 84 individuals were aware of the firm’s new brand. a) Construct a 95% confidence interval for the proportion of individuals in the target market segment who are aware of the firm’s new brand. b) The manager in charge of the new brand has stated that the brand awareness is greater than .75, meaning that more than 75% of the population is aware of the brand. He would like to use hypothesis testing to proof his claim. At the 5% significance level, conduct a hypothesis test with the goal of proofing his claim. In particular i) specify the null hypothesis and the alternative hypothesis ii) whether you are using one or two tailed test iii) the p-value of the test iv) the results of the test, “in English”. Hints: i) Think carefully about what is the null and what is the alternative ii) if you want to use StatTools for the analysis, you need to create the survey data, that is create a column in Excel containing the responses from the 125 individuals (as zeros and ones), then you can run the analysis in a similar manner to what we did in class for the sample mean. For future polls, the firm is interested in minimizing their marketing research costs. The margin of error in their pools should be no larger than B (i.e., 100B percentage points). To simplify the analysis, we will assume their marketing study only has a single question that is used to estimate p, at the 5% significance level. c) If the firm had no prior knowledge of p, how large would the sample size have to be to ensure MOE ≤ B? (Hint: your answer will be a function of B). d) The firm has prior knowledge that p will likely be somewhere between .10 and .20 (that is between 10% and 20%). How large should the sample be if they would like to ensure that MOE (=B) is no larger than 0.01 or 1%.
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