Estimating and Testing Proportions for Market Research and Sample Size Determination

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Estimating and Testing Proportions for Market Research and Sample Size DeterminationA consumer products firm has recently introduced a new brand. The firm would like to estimatethe proportion of people in its target market segment who are aware ofthe new brand. As part ofa larger market research study, it was found that in a sample of 125 randomly selectedindividuals 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 marketsegment 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.Here we need the 95% confidence interval for the population proportion which is,95% CI =ቆ𝑝̂±𝑍0.025∗ට𝑝ො∗(1−𝑝ො)𝑛ቇ=ቆ8ସ125±1.96∗ට8ర125∗ቀ1−8ర125ቁ125ቇ= (0.5897, 0.7543)b.The manager in charge of the new brand has stated that the brand awareness is greaterthan .75, meaning that more than 75% of the population is aware of the brand. He wouldlike to use hypothesis testing to prove his claim. At the 5% significance level, conduct ahypothesis test with the goal of proving his claim. In particulari)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, andiv)Providethe results of the test in “plain English”.Hints: 1) Think carefully about what is the null hypothesis, and what is the alternative. 2) If youwant to use StatToolsfor the analysis, you need to create the survey data in Excel first; then youcan run the analysis.Here we want to test whether the brand awareness is more than 0.75 or not thus the hypothesesare,𝐻0:𝑝≤0.75𝑎𝑛𝑑𝐻𝑎:𝑝>0.75From the alternative hypothesis we can see that this is one tailed (right tailed) test for the singleproportion thus the Z test for proportion is the best test to use.Test Statistic =8ర125−0.75ට0.75∗(1−0.75)125=−2.01

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