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. If you use Excel and/or StatTools, please specify any functions you use and all the inputs.
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 prove his claim. At the 5% significance level, conduct a hypothesis test with the goal of proving his claim. In particular
i) specify the null hypothesis and the alternative hypothesis,
ii) state whether you are using a one- or two-tailed test,
iii) specify the p-value of the test, and
iv) provide the results of the test in "plain English".