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An employer collected data from its employees on whether or not they stay up late and whether or not they drink coffee. The two-way table below shows the data collected.

Stays Up Late Does Not
Stay Up Late Total
Drinks Coffee 18 9 27
Does Not
Drink Coffee 6 17 23
Total 24 26 50

Which correlation does the two-way table suggest?
A.
Those who do not stay up late tend to drink coffee.

B.
Those who do not stay up late tend not to drink coffee.

C.
None of the correlations listed are correct.

D.
Those who stay up late tend not to drink coffee.

1 answer

To analyze the two-way table:

  • Total number of employees: 50
  • Employees who stay up late and drink coffee: 18
  • Employees who stay up late and do not drink coffee: 9
  • Employees who do not stay up late and drink coffee: 6
  • Employees who do not stay up late and do not drink coffee: 17

Now, let's summarize the data:

  • Stays Up Late:

    • Drinks Coffee: 18
    • Does Not Drink Coffee: 9
    • Total: 27

  • Does Not Stay Up Late:

    • Drinks Coffee: 6
    • Does Not Drink Coffee: 17
    • Total: 23

From the table:

  • The ratio of employees who stay up late and drink coffee (18) versus those who stay up late and do not drink coffee (9) shows that more employees who stay up late do drink coffee.
  • In contrast, employees who do not stay up late are more likely to not drink coffee (17 out of 23).

Now let's evaluate the correlation options based on the table:

A. Those who do not stay up late tend to drink coffee.

  • This is not supported by the data. Only 6 of the 23 who do not stay up late drink coffee.

B. Those who do not stay up late tend not to drink coffee.

  • This is supported by the data (17 do not drink coffee out of 23 who do not stay up late).

C. None of the correlations listed are correct.

  • This is not true since option B is correct.

D. Those who stay up late tend not to drink coffee.

  • This is not supported by the data, as higher numbers drink coffee.

Based on this analysis, the best answer is:

B. Those who do not stay up late tend not to drink coffee.