Three hundred tenured professors at Florida Universities are randomly sampled and are asked: “On what day of the week were you born?” The results are in the table below. Assuming that each weekday has an equal theoretical probability, which day of the week has the most unusual observed frequency in this sample?
Day Sun Mon Tue Wed Thu Fri Sat
Count 36 42 60 42 57 30 33
To determine which day of the week has the most unusual observed frequency in this sample, we first need to calculate the expected frequency for each day of the week if the distribution was uniform (equal theoretical probability).
There are 7 days in a week, so the expected frequency for each day of the week would be:
Expected Frequency = Total count / Number of days = 310 / 7 = 44.29
Now, we can compare the observed frequency with the expected frequency to see which day has the most unusual observed frequency.
For each day of the week:
- Sun: |36 - 44.29| = 8.29
- Mon: |42 - 44.29| = 2.29
- Tue: |60 - 44.29| = 15.71
- Wed: |42 - 44.29| = 2.29
- Thu: |57 - 44.29| = 12.71
- Fri: |30 - 44.29| = 14.29
- Sat: |33 - 44.29| = 11.29
The largest difference between observed and expected frequency is for Tuesday (15.71), making Tuesday the day of the week with the most unusual observed frequency in this sample.