A company has recently introduced a new hardware 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 150 randomly selected individuals from the target market segment, 101 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 0.6, meaning that more than 60% of the population is aware of the brand. At the 5% significance level, conduct a hypothesis test with the goal of proving his claim. a. Specify the null hypothesis and the alternative hypothesis. Define the parameter of your interest and write the mathematical expressionsof your hypotheses in terms of your parameter (Statements in English are NOT acceptable). b. State Type I & II errors i
A company has recently introduced a new hardware 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 150 randomly selected individuals from the target market segment, 101 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 0.6, meaning that more than 60% of the population is aware of the brand. At the 5% significance level, conduct a hypothesis test with the goal of proving his claim.
a. Specify the null hypothesis and the alternative hypothesis. Define the parameter of your interest and write the mathematical expressionsof your hypotheses in terms of your parameter (Statements in English are NOT acceptable).
b. State Type I & II errors in plain English within the context of the problem.
c. Use StatTools to conduct the hypothesis test. You need to create the summary table of the survey data in Excel first; then you can run the analysis.
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- Copy and paste the report generated by StatTools.
- Report the p-value
d. At the 5% significant level, provide the results of the test in plain English within the context of the problem (interpretation of "Reject"/"Don't Reject" in English).
e. Construct a 95% confidence interval estimate for the population proportion of people who are aware of the new hardware brand. Copy and paste the report generated by StatTools. Interpret the confidence interval within the context of the problem in English.
f. For future polls, the firm is interested in minimizing their marketing-research costs. The margin of error (MOE) in their pools should be no larger than B(i.e., ± 100B percentage points). To simplify the analysis, we will assume that their marketing study only has a single question that is used to estimate the proportion, p at the 95% confidence level. Based on the results in part d, estimate the
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