The two-way table shows the results from a survey of dog and cat owners about whether their pet prefers dry food or wet food.

Efan Halliday

Efan Halliday

Answered question

2020-12-03

The two-way table shows the results from a survey of dog and cat owners about whether their pet prefers dry food or wet food.
 Dry  Wet  Cats 1030 Dogs2020
Does the two-way table show any difference in preferences between dogs and cats? Explain.

Answer & Explanation

izboknil3

izboknil3

Skilled2020-12-04Added 99 answers

Given:
 Dry  Wet  Total  Cats 1030 Dogs2020Total
Let us first determine the cumulative frequencies which are obtained by adding the frequencies in the corresponding column or the corresponding row.
 Dry  Wet  Total  Cats 103010+30=40 Dogs202020+20=40Total10+20=3030+20=5040+40=80
Next, we determine the percentages by dividing the frequency by the row total for the cells not in the last column, while we divide the frequency by the table total for the cells in the last column.
 Dry  Wet  Total  Cats 10(1040=0.25=25%)30(3040=0.75=75%)40(4080=0.5=50%) Dogs20(2040=0.5=50%)20(2040=0.5=50%)40(4080=0.5=50%)Total30(3080=0.375=35.5%)50(5080=0.625=62.5%)80(8080=1=100%)
We note that 75% of the cats prefer the wet food, while 50% of the dogs prefer the wet food. This then implies that there appears to be a different, in the preferences of dogs and cats as the percentages 75% and 50% differ a lot.
Answer: YES

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