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Below are the data collected from two random samples of 500 American adults on the number of hours they spend doing leisure and sports activities per
day (rounded to the nearest hour)
Number of hours spent doing leisure and sports activities per day
Sample A: Number of adults
70 90 135 140 65
Sample B: Number of adults
80 80 130 135 75

Dan concludes that adults spend a mean of 3 hours each day doing leisure and sports activities. Bret thinks the mean is 4 hours. Who is correct-Dan or Bret?
Explain your answer in two or three sentences. Make sure to use facts to support your answer.

Sagot :

okpalawalter8

Dan is Correct by concluding  that adults spend a mean of 3 hours each day doing leisure and sports activities. because [tex]3.08[/tex] hours or [tex]3.09[/tex] hours which are the mean time of sample A and B  is approximately equal to 3 hours

From the question we are told that:

Total Sample size [tex]n=500[/tex]

Dan's mean  [tex]\=x_D= 3hr[/tex]

Bret's mean   [tex]\=x_D= 4hr[/tex]

Generally, the  Total hours spent doing leisure and sports activities  is mathematically given by

For Sample A

[tex]T_a=(1*70)+(2*90)+(3*135)+(4*140)+(5*65)\\\\[/tex]

[tex]T_a=1540 hours[/tex]

For Sample B

[tex]T_b=(1*80)+(2*80)+(3*130)+(4*135)+(5*75)[/tex]

[tex]T_b=1545[/tex]

Therefore

Mean Time spent doing leisure and sports activities by an American Adult

For Sample A

[tex]T_A=\frac{T_a}{n}[/tex]

[tex]T_A=\frac{1540}{500}[/tex]

[tex]T_A=3.08[/tex] hours

[tex]T_A \approx 3[/tex] hours

For Sample B

[tex]T_A'=\frac{T_b}{n}[/tex]

[tex]T_A'=\frac{1545}{500}[/tex]

[tex]T_A'=3.09[/tex] hours

[tex]T_A' \approx 3[/tex] hours

In conclusion

Dan is Correct because [tex]3.08[/tex] or [tex]3.09[/tex] which are the mean time of sample A and B is approximately equal to [tex]3[/tex]

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