Market Changes Very Little: The company should try to improve snack N, because current snacks consumers prefer current leader, L. Market Changes Very Rapidly: The company should market snack N to the group of new consumers, because they prefer snack N over the current leader, L.
Practice makes perfect
We want to know what actions the company should take in light of changes in the snack market. To identify and explain the best possibilities we will find the preferences of Current L Consumers and Not Current L Consumers. First look at the two-way table with the results of the survey.
Prefer L
Prefer N
Current L Consumer
72
46
Not Current L Consumer
52
114
We have to construct a two-way table of relative frequencies and find conditional probabilities to find the best strategy for the company.
Making a Two-Way Table of Frequency Counts
At first we will use the given table of joint frequencies to calculate the marginal frequencies. To do so we will sum the values in the columns and rows.
Prefer L
Prefer N
Total
Current L Consumer
72
46
124
Not Current L Consumer
52
114
160
Total
118
166
284
Now we know the marginal frequencies and the total number of surveyed people, which is 44.
Let's evaluate these expressions and round the results to the nearest hundredths.
Prefer L
Prefer N
Total
Current L Consumer
0.25
0.16
0.44
Not Current L Consumer
0.18
0.4
0.56
Total
0.42
0.58
1
Recommendations if Market Changes Very Little
Finally, we will find the conditional probability of preferring snack N for each group. Let's remember the formula for the conditional probability.
P(B|A)=P(AandB)/P(A)
Event B in the formula is preferring snack N, and event A is choosing the participant from group A. We will divide the joint relative frequency from the column Prefer N by the marginal frequency in the corresponding row to get the conditional probability for each group. We will start with Current L Consumers.
P(Current L Consumer and Prefer N)/P(Current L Consumer)
Based on the sample, we obtained that Current L Consumer will Prefer N with a probability of 0.36. This means that the company should try to improve snack N if they expect the snack market to change very little, because most of the current snack consumers prefer snack L.
Recommendations if Market Changes Very Rapidly
Now we will repeat these calculations for Not Current L Consumers.
P(Not Current L Consumer and Prefer N)/P(Not Current L Consumer)
Based on the sample, we obtained that Not Current L Consumer will Prefer N with a probability of 0.72. This means that if the company expects the snack market to expand rapidly, they should market it in the group of new snack consumers.
