Question

Asked Sep 16, 2019

3. A national retailer has completed an internal survey on its social media strategy. The key question in the survey is whether the stores managers think that the recently launched social media strategy is effective. The following is the output of a statistical analysis of the data:

Social media Strategy is effective Store Managers No Yes

Vancouver 40 55

Manitoba 20 35

Alberta 15 35

Based on this output, can the retailer conclude that the opinion of the store managers on the whether the recently launched social media strategy is effective is dependent on which region they belong to? Use a chi square test and a level of significance of 0.05

Step 1

Let us first test whether “the opinion of the store manager” and “the region they belong to” are independent or not, using a Chi-square test of Independence. If the two variables are found not to be independent, then, by observing the change in the proportions, it can be decided whether the opinion of store manager is dependent on the region they belong to.

Step 2

**Hypotheses:**

The null hypothesis is:

*H*_{0} : The opinion of store manager and the region they belong to did not attribute differently.

The alternative hypothesis is:

*H*_{1} : The opinion of store manager and the region they belong to attribute differently.

Step 3

**Calculation steps:**

The calculations have been done in EXCEL.

Denote *oij* as the observed frequency for *i*th row and *j*th column (*i* =1, 2;* j* =1, 2) and *eij* as the expected frequency for *i*th row and *j*th column.

Table 1 provides the data values, *oij*.

Table 2 calculates the row proportions: (cell value)/(row total) = *oij* / *oi∙* so that, the first row proportion will be 40/95 ≈ 0.4211. Similarly, the others can be calculated.

Table 3 calculates the expected frequencies under the independence assumption. If independent, ...

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