Final answer:
To find the value of the test statistic, calculate the expected frequencies for each group based on the totals given, then use these with the observed frequencies to compute the chi-square test statistic. The detailed computation is not provided without further calculation.
Step-by-step explanation:
To determine if brand perception is dependent on age using the provided data, we should perform a chi-square test for independence. In this test, the null hypothesis is that brand perception is independent of age groups, and the alternative hypothesis is that there is a dependency.
First, we calculate the expected frequencies for each cell in the table, using the formula:
Expected frequency = (Row total × Column total) / Grand total
After calculating expected frequencies for each cell, the test statistic is computed using the formula:
χ2 = Σ [(Observed frequency - Expected frequency)2 / Expected frequency]
Once we have the observed frequencies (from the data given) and the expected frequencies (calculated), we plug these numbers into the formula and sum all resulting values to get the chi-square test statistic. This calculated test statistic is then compared with the critical value from the chi-square distribution table at a certain significance level to determine if we reject the null hypothesis or not.
Since the specific expected frequencies and the calculation of the chi-square test statistic are not provided in the question, the direct answer with the test statistic value cannot be given without further computation.