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Estimating and Testing Proportions for Market Research and Sample Size Determination

Analysis of proportion estimation and sample size determination in market research.

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    Estimating and Testing Proportions for Market Research and Sample Size Determination 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. Here we need the 95% confidence interval for the population proportion which is, 95% CI = ቆ 𝑝 ̂ ± 𝑍 0 . 025 ∗ ට 𝑝 ො ∗ ( 1 − 𝑝 ො ) 𝑛 ቇ = ቆ 8ସ 125 ± 1 . 96 ∗ ට 8ర 125 ∗ ቀ 1 − 8ర 125 ቁ 125 ቇ = (0.5897, 0.7543) 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”. Hints: 1) Think carefully about what is the null hypothesis, and what is the alternative. 2) If you want to use StatTools for the analysis, you need to create the survey data in Excel first; then you can run the analysis. Here we want to test whether the brand awareness is more than 0.75 or not thus the hypotheses are, 𝐻 0 : 𝑝 ≤ 0 . 75 𝑎𝑛𝑑 𝐻 𝑎 : 𝑝 > 0 . 75 From the alternative hypothesis we can see that this is one tailed (right tailed) test for the single proportion thus the Z test for proportion is the best test to use. Test Statistic = 8ర 125 − 0 . 75 ට 0 . 75 ∗ ( 1 − 0 . 75 ) 125 = − 2 . 01

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