A consumer products firm has recently introduced a new brand. The firm would like to estimate the proportion of people ...

     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%.