To determine the mean number of hours American students spend in school per day, we need to calculate the weighted average based on the data provided.
For Meg's conclusion:
Mean hours = (4*70 + 5*100 + 6*125 + 7*135 + 8*70) / (70 + 100 + 125 + 135 + 70)
Mean hours = (280 + 500 + 750 + 945 + 560) / 500 = 3035 / 500 = 6.07 hours
Therefore, Meg's conclusion is incorrect.
For Tara's conclusion:
Mean hours = (4*80 + 5*90 + 6*120 + 7*125 + 8*85) / (80 + 90 + 120 + 125 + 85)
Mean hours = (320 + 450 + 720 + 875 + 680) / 500 = 3045 / 500 = 6.09 hours
Therefore, Tara's conclusion is also incorrect.
Based on the calculations, the mean number of hours American students spend in school per day is actually 6.07 hours, which is closer to Tara's estimate. Neither Meg nor Tara is entirely correct, but Tara's estimate of 6 hours is the closest to the actual mean calculated from the data provided.
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.(10 points)
3 answers
Explain it in 3 sentences
Tara's estimate of 6 hours is closer to the actual mean of 6.07 hours calculated from the data collected from the samples of American students. Therefore, Tara's conclusion is more accurate than Meg's conclusion of 7 hours. Both students were close in their estimates, but Tara's estimation was slightly more accurate based on the provided data.