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.

The manager in charge of the new brand has stated that the brand awareness is greater than 0.75, meaning that more than 75% of the population is aware of the brand. At the 5% significance level, conduct a hypothesis test with the goal of proving his claim.

1. Specify the null hypothesis and the alternative hypothesis. State whether you are using a one- or two-tailed test and explain your reasoning.
2. Conduct calculations by hand to compute the critical value and p-value of the test. Determine your decision using two methods,the rejection regionandthe p-value approach.
3. Use R to conduct the hypothesis test. Copy and paste the command and report generated by R.
4. Communicate the results of the test in "plain English" including the meaning of the p-value.