A running coach wants to know if participating in weekly running clubs significantly improves the time to run a mile. The runnin
g coach collects mean mile times for 42 runners who participate in weekly running clubs with 54 runners who do not run in clubs. The running coach measures times in January and June of the same year. All times are in seconds, and the runners all started with mile times between 8 minutes (480 seconds) and 9 minutes (540 seconds). Here are the results:
January June Change
Mean (seconds) StDev (seconds) Mean (seconds) StDev (seconds) Mean (seconds) StDev (seconds)
Running Club N = 42 530 28 520 23 10 4
Not in a Club N = 54 527 25 519 22 8 3
What is the best method for the running coach to use to determine if participating in weekly running clubs significantly improves the time to run a mile?
A) Use the difference in sample means (530 – 520) in a hypothesis test for a difference in two population means.
B) Use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means.
C) Use the sample mean 10 in a hypothesis test for a population mean.
January June Change
Mean (seconds) StDev (seconds) Mean (seconds) StDev (seconds) Mean (seconds) StDev (seconds)
Running Club N = 42 530 28 520 23 10 4
Not in a Club N = 54 527 25 519 22 8 3
What is the best method for the running coach to use to determine if participating in weekly running clubs significantly improves the time to run a mile?
A) Use the difference in sample means (530 – 520) in a hypothesis test for a difference in two population means.
B) Use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means.
C) Use the sample mean 10 in a hypothesis test for a population mean.
1 answer:
Answer:
Option B is correct.
Use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means.
Step-by-step Explanation:
The clear, complete table For this question is presented in the attached image to this solution.
It should be noted that For this question, the running coach wants to test if participating in weekly running clubs significantly improves the time to run a mile.
In the data setup, the mean time to run a mile in January for those that participate in weekly running clubs and those that do not was provided.
The mean time to run a mile in June too is provided for those that participate in weekly running clubs and those that do not.
Then the difference in the mean time to run a mile in January and June for the two classes (those that participate in weekly running clubs and those that do not) is also provided.
Since, the aim of the running coach is to test if participating in weekly running clubs significantly improves the time to run a mile, so, it is logical that it is the improvements in running times for the two groups that should be compared.
Hence, we should use the difference in sample means (10 and 8) in a hypothesis test for a difference in two population means.
Hope this Helps!!!
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9514 1404 393
Answer:
(b) 15.32
Step-by-step explanation:
You can use your triangle sense to answer this.
The side x will always be shorter than the hypotenuse, 20. This eliminates the last two choices.
If the angle is 45°, then the sides are equal at about 0.707 times the length of the hypotenuse. That would make them 0.707×20 = 14.14. Since the angle is greater than 45°, the opposite side will be greater than 14.14. Only one answer choice fits between 14 and 20: the second choice -- 15.32.
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The mnemonic SOH CAH TOA reminds you of the relation ...
Sin = Opposite/Hypotenuse
sin(50°) = x/20
x = 20×sin(50°) . . . . multiply by 20 to find x
x ≈ 15.32 . . . . . . . . . use your calculator to evaluate
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The attachment is intended to show how the triangle side lengths change with angle.
