Is Gender Linked to Brand Preferences According to Chi-Square Analysis?

[sumans]

The following table shows brand preferences against gender on the basis of a random sample of size 100 from population. It is intended to examine possible association between gender and brand preferences.

Brand A Brand B
Men 30 20
Women 20 30

At 5% level of significance will you conclude that gender and brand preferred are independent? It is given that the table value of the Chi-Square distribution with right tail area equal to 5% for 1, 2 and 3 degrees of freedom are 3.84, 5.99 and 7.81 respectively.

 

[Krusty]

This forum isn't for homework questions. If you're trying to get questions answered at least show your attempts at the questions. No-one is going to give you the answer straight up, but someone may give you some guidance if you show an attempt that is heading in the right direction

 

[tacman]

Based on the given data, it appears that there may be a possible association between gender and brand preferences. However, in order to determine if this association is significant, we can use the Chi-Square test. This test measures the difference between the observed frequencies and the expected frequencies, assuming that there is no association between the variables.

In this case, our null hypothesis would be that gender and brand preferences are independent, meaning that there is no relationship between the two variables. Our alternative hypothesis would be that there is a significant association between gender and brand preferences.

To conduct the Chi-Square test, we would first calculate the expected frequencies for each cell in the table. This can be done by multiplying the row total by the column total and dividing by the total sample size. In this case, the expected frequencies for the first cell (men who prefer brand A) would be (30+20)(30+20)/100 = 25. Similarly, the expected frequencies for the other cells can be calculated.

Next, we would calculate the Chi-Square statistic by using the formula: Σ (O-E)^2/E, where O is the observed frequency and E is the expected frequency. This would give us a Chi-Square value of 5.6.

Now, we can compare this value to the critical values given in the question. Since we have 1 degree of freedom (since we are only comparing two categories), the critical value is 3.84. Since our calculated Chi-Square value is greater than the critical value, we can reject the null hypothesis and conclude that there is a significant association between gender and brand preferences at a 5% level of significance.

In conclusion, based on the given data and using the Chi-Square test, we can conclude that there is a significant association between gender and brand preferences. However, further analysis and research may be needed to understand the nature and strength of this association.