Marketing Research Homework - Fall 100 Points

Marketing Research Homework Fall 2015100 Points

1. The current advertising campaign for a major soft drink brand would be changed if less than 30 percent of the consumers like it. A random sample of 300 consumers was surveyed, and 84 respondents indicated that they liked the campaign. Should the campaign be changed based on your statistical test?

2. A major department store chain is having an end-of-season sale on refrigerators. The number of refrigerators sold during this sale at a sample of 10 stores was: Is there evidence that an average of more than 50 refrigerators per store were sold during this sale? a. What is the sample mean? What is the standard deviation? (6 points) b. What is the standard error and confidence interval (8 points) c. What is the t statistic? (4 points) What is your conclusion? (2 points)

3. McDonald’s is testing the impact of a new menu on the store traffic of its franchise. It recorded the store traffic of 7 randomly selected stores across the nation. The store traffic is recorded during the first Wednesday before and after the new menu’s introduction. The same store is recorded twice with old menu and with new menu. The store traffics are recorded on each of the seven stores as follows: (Cell values are average number of visitors per hour between 9am -6pm). Store ID, New menu (Tnew), Old menu (Told), Difference. Is there a significant difference in store traffic between the old menu and new menu conditions? (1) Find the average difference of the store traffic between the two menus. (5 points) (2) Find the standard deviation and standard error of the average difference. (5 points) (3) What is the confidence interval of the difference? (5 points) (4) Find the t value of the study. (3 points) (5) Given the t critical value of 2.45, state the conclusion. (2 points)

Paper For Above instruction

Statistical hypothesis testing plays a crucial role in marketing research, facilitating data-driven decision making across various scenarios. This paper systematically examines three marketing research problems, applying statistical techniques to determine whether observed sample data support certain business decisions.

1. Soft Drink Campaign Approval

The first scenario involves assessing whether the current advertising campaign for a major soft drink should be altered based on consumer preference. The hypothesis test examines if fewer than 30% of consumers like the campaign. Given a sample size of 300 consumers, with 84 expressing liking the campaign, the sample proportion is p̂ = 84/300 = 0.28. The null hypothesis (H₀) states that the true proportion p = 0.30, whereas the alternative hypothesis (H₁) asserts p

z = (p̂ - p₀) / √[p₀(1 - p₀) / n] = (0.28 - 0.30) / √[0.30(0.70) / 300] ≈ -0.02 / 0.02525 ≈ -0.791

At a 5% significance level, the critical z-value for a left-tailed test is approximately -1.645. The calculated z = -0.791 does not fall into the rejection region (z

2. Refrigerator Sales Analysis

This problem assesses whether the mean number of refrigerators sold per store exceeds 50. Given data for 10 stores, the sample mean (x̄) and standard deviation (s) are first computed. Suppose the data sales are: 55, 47, 52, 49, 60, 53, 48, 51, 54, 56. Calculating the sample mean:

x̄ = (55 + 47 + 52 + 49 + 60 + 53 + 48 + 51 + 54 + 56) / 10 = 50.5

Standard deviation (s) calculation yields approximately 4.78. The standard error (SE) is:

SE = s / √n = 4.78 / √10 ≈ 1.51

Constructing a 95% confidence interval using the t-distribution (degrees of freedom = 9), with t* ≈ 2.262, the interval is:

CI = x̄ ± t* × SE = 50.5 ± 2.262 × 1.51 ≈ 50.5 ± 3.42, so (47.08, 53.92)

To test whether the mean exceeds 50, the t-statistic is:

t = (x̄ - μ₀) / (s / √n) = (50.5 - 50) / 1.51 ≈ 0.33

Since t = 0.33

3. Impact of New Menu on Store Traffic

This analysis involves paired sample data from 7 stores, attempting to determine if the new menu significantly affects store traffic. Suppose the data are:

The average difference is:

Mean difference = (15 + 5 + 8 + 3 + 7 + 4 + 6) / 7 ≈ 6.29

The sample standard deviation of the differences is calculated to be approximately 3.55. The standard error of the mean difference is:

SE = s / √n = 3.55 / √7 ≈ 1.34

The 95% confidence interval for the mean difference (using t* ≈ 2.447 for 6 degrees of freedom) is:

CI = 6.29 ± 2.447 × 1.34 ≈ 6.29 ± 3.28, so (3.01, 9.57)

The t-statistic for testing if the mean difference is zero:

t = (6.29 - 0) / 1.34 ≈ 4.69

Given the critical t value of 2.45, since 4.69 > 2.45, we reject the null hypothesis. There is significant evidence to suggest that the new menu significantly increases store traffic.

Conclusion

Statistical hypothesis testing enables marketers and business managers to base critical decisions on empirical evidence. In the soft drink campaign assessment, the lack of sufficient evidence indicates that the campaign's approval should remain unchanged. For refrigerator sales, the data do not support the claim that stores sell more than 50 units on average during the sale. Meanwhile, the analysis of store traffic reveals a significant increase associated with the new menu. These examples illustrate the importance of proper data collection, hypothesis formulation, and analysis in effective marketing decision-making.

References

• Cochran, W. G. (1977). Sampling Techniques. John Wiley & Sons.
• Gelman, A., & Hill, J. (2007). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
• Levine, D. M., Krehbiel, T. C., & Berenson, M. L. (2012). Statistics for Management. Pearson.
• Moore, D. S., McCabe, G. P., & Craig, B. A. (2014). Introduction to the Practice of Statistics. W.H. Freeman.
• Snedecor, G. W., & Cochran, W. G. (1989). Statistical Methods. Iowa State University Press.
• Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics. Sage.
• Weiss, N. A. (2012). Introductory Statistics. Pearson.
• Ott, R. L., & Longnecker, M. (2010). An Introduction to Statistical Methods and Data Analysis. Brooks/Cole.
• Tabachnick, B. G., & Fidell, L. S. (2013). Using Multivariate Statistics. Pearson.
• Fowler, F. J. (2014). Survey Research Methods. Sage.