Introduction
Hypothesis testing is an important aspect in marketing research while test of research findings’ significance is critical for determining their reliability. To demonstrate the hypothesis testing process and application of significance test, this analysis uses the case of Bentley Foods that conducted a survey on 1000 customers to identify whether at least 15% of the customers would prefer the new line of pizza over other pizza for the company to start producing and marketing the product. From the survey, Bentley identified that 172 customers would prefer the new pizza. In that respect, this analysis applies the case to demonstrate hypothesis testing, calculation of standard error of a sample proportion, Z-statistic and critical proportion calculation as well as interpretation of the findings at a significance level of 0.05.
Body
- Null and alternative hypotheses
Hypothesis testing requires stating of both null and alternative hypotheses in a way that they are mutually exclusive. In that respect, one has to be true for the other to be false. (Lacobucci & Churchill, 2010) Thus, the hypotheses to be tested for Bentley Foods are as noted below.
- Null Hypotheses: At least 15% of the population prefers the new line of frozen pizza.
- Alternative Hypotheses: Less than 15% of the population prefers the new line of frozen pizza.
- Standard error of the proportion
The formula for calculating standard error for a sample proportion is SE = ((p*(1-p) / n) ½ where p is the sample proportion and n is the sample size. (Lacobucci & Churchill, 2010) Thus, given that p = 172/1000 and n = 1000 as the values for Bentley Food’s test, the standard error of the proportion is as calculated below
p = (172 / 1000) = 0.172
1-p = (1-0.172) = 0.828
SE = ((0.172*(0.828) / 1000)) ½ = (0.142416) 1/2 = 0.3773804
SE = 0.3773804
- Z-statistic and the probability of obtaining the statistic if null hypothesis is true
The formula for calculating Z-statistic is ((p – P) / SE)) where p is the sample proportion, P represents proportion of the population that should prefer the new line of Pizza for the Bentley Foods to start producing and marketing it and SE is the standard error of the proportion. (Triola, 2010)
Thus, given p = 0.172, P = 0.15 and SE = 0.3773804
Z- Statistic = ((0.172 - 0.15) / 0.3773804) = (0.022 / 0.3773804) = 0.58312
On the other hand, the probability of getting the Z-Statistic of 0.58312 given that null hypothesis is true is equivalent to the p-value of the sample proportion. Using a normal standard distribution table or a calculator, the p-value is calculated to be 0.93885. (Waters, 2011)
- Decision on null hypotheses using .05 significant level
Using a.05 significance level and given that the p-value of 0.93885 is greater than the .05 significance level, the null hypothesis is accepted as being true. In that respect, it is accepted that the test results that more than 15% prefers the new line of pizza is significant for Bentley Foods to start producing and marketing the product. (Lacobucci & Churchill, 2010)
- Sample proportion at .05 significance level
At .05 significant level and given that Z- value = ((p-P) / SE), the Z critical value is 1.96 as calculated from standard distribution tables with the formula [InvNorm((1-Significance level)/2)]. (Robert & Elliot, 2006) In that respect, the critical sample proportion p is calculated as (1.96*0.3773804) + 0.15 = 0.8896.
Conclusion
In view of the analysis, the results that 172 out of the 1000 customers involved in Bentley Foods survey would prefer the Company’s new line of pizza has been demonstrated as being significant at a significance level of 0.05. This is given that the Z-statistic of 0.58312 is greater than .05 hence null hypotheses is accepted as being true which means that Bentley can start producing and marketing the new line of pizza.
References
Lacobucci, D. & Churchill, G. (2010). (10th Ed.). Marketing Research: Methodical
Foundations. Ohio: South-Western College Publishers.
Robert, V. & Elliot, A. (2006). Probability and Statistical Inference. New Jersey: Pearson
Prentice.
Triola, M.F. (2010). (4th Ed.). Essentials of Statistics. New Jersey: Pearson Publishers.
Waters, D. (2011). (5th Ed.). Quantitative methods for Business. New Jersey: Pearson
Publishers.
