Question

(08.01 MC)Below are the data collected from two random samples of 500 American students on the number of hours they spend in school per day (rounded to the nearest hour):
Number of hours in school per day 4 5 6 7 8
Sample A: Number of students 70 100 125 135 70
Sample B: Number of students 80 90 120 125 85


Meg concludes that students spend a mean of 7 hours in school each day. Tara thinks the mean is 6 hours. Who is correct—Meg or Tara? Explain your answer in two or three sentences. Make sure to use facts to support your answer.

Answer 1

Answer:

The mean time spent in school is approximately 6 hours each day and Tara is correct

Step-by-step explanation:

The given data is presented here as follows;

Number of hours in school per day,      4,        5,        6,        7,         8

Sample A:,                                               70       100    125      135       70

Sample B:,                                               80        90     120     125      85

For sample A, we have;

The total number of hours spent by sample A = 4 × 70 + 5 × 100 + 6 × 125 + 7 ×135 + 8 ×70 = 3035 hours

The number of students in sample A = 70 + 100 + 125 + 135 + 70 = 500

The mean number of hours spent in school by sample A = 3035 /500 = 6.07

For sample B, we have;

The total number of hours spent by sample A = 4 × 80 + 5 × 90 + 6 × 120 + 7 ×125 + 8 ×85 = 3045 hours

The number of students in sample A = 80 + 90 + 120 + 125 + 85 = 500

The mean number of hours spent in school by sample A = 3045 /500 = 6.09

The cumulative data, we have;

(3035 + 3045)/1000 = 6.08

Therefore, the mean is approximately 6 hours each day and Tara is correct.