Fill in the blank in the sample below if the variables are independent in the sample
like product do not like product
old 10 7
young 40
It would help if you proofread your questions before you posted them. You only have one value for the young.
The independent variable is age, but it would be better if you more specifically defined the age ranges.
I hope this helps.
To determine if the variables are independent in the sample, you need to calculate the expected values for each category. The expected value is the value you would expect to see if the variables were independent.
First, you can calculate the total count for each row and column:
- Row Total for "like product": 10 + 7 = 17
- Row Total for "do not like product": 40
- Column Total for "old": 10 + 40 = 50
- Column Total for "young": 7
Next, you can calculate the expected value for each category by multiplying the row total by the column total and dividing by the total count:
- Expected value for "old" and "like product": (17 * 50) / 57 = 14.912
- Expected value for "old" and "do not like product": (40 * 50) / 57 = 35.088
- Expected value for "young" and "like product": (17 * 7) / 57 = 2.088
- Expected value for "young" and "do not like product": (40 * 7) / 57 = 4.912
Now, you can compare the expected values to the observed values to see if they are similar. If they are similar, it suggests that the variables are independent. If they are different, it suggests that there may be a relationship between the variables.
In this case, you need to fill in the blank for the category "young" and "do not like product". The observed value for this category is 40. Based on the calculations above, the expected value is 4.912. Since the observed value (40) is significantly different from the expected value (4.912), it suggests that the variables are not independent in the sample.
Therefore, the blank for the category "young" and "do not like product" is 40.