A certain paper describes a study of the possible cardiovascular benefits of active video games. Mean heart rate for healthy boys ages 10 to 13 after walking on a treadmill at 2.6 km/hour for 6 minutes is known to be 98 beats per minute (bpm). For each of 14 boys in this age group, heart rate was measured after 15 minutes of playing Wii Bowling. The resulting sample mean and standard deviation were 103 bpm and 15 bpm, respectively. Assume that the sample of boys is representative of boys age 10 to 13 and that the distribution of heart rates after 15 minutes of Wii Bowling is approximately normal. Does the sample provide convincing evidence that the mean heart rate after 15 minutes of Wii Bowling is different from the known mean heart rate after 6 minutes walking on the treadmill? Carry out a hypothesis test using α = 0.01.

Question

Mathematics

Helena Cisneros

9 May, 22:10

A certain paper describes a study of the possible cardiovascular benefits of active video games. Mean heart rate for healthy boys ages 10 to 13 after walking on a treadmill at 2.6 km/hour for 6 minutes is known to be 98 beats per minute (bpm). For each of 14 boys in this age group, heart rate was measured after 15 minutes of playing Wii Bowling. The resulting sample mean and standard deviation were 103 bpm and 15 bpm, respectively. Assume that the sample of boys is representative of boys age 10 to 13 and that the distribution of heart rates after 15 minutes of Wii Bowling is approximately normal. Does the sample provide convincing evidence that the mean heart rate after 15 minutes of Wii Bowling is different from the known mean heart rate after 6 minutes walking on the treadmill? Carry out a hypothesis test using α = 0.01.

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Wade Keith · Answer 1

No, the claim is not supported by the sample evidence

Step-by-step explanation:

We will compare the mean heart rate of the boys playing Wii bowling to the heart rate of boys who ran on a treadmill.

We have:

µ = 98 (boys on treadmill)

σ = unknown or not given

x = 103 (boys playing Wii)

s = 15

n = 14

H0: µ = 98

Ha: µ ≠ 98 (claim)

We will run a hypothesis test at the 0.01 level of significance.

Since n < 30, our critical values will be a t-value.

This is a 2 tailed test, so our critical regions are

t 3.012

If the test statistic falls in either of these regions, we will reject the null hypothesis