Determine which of the following statements is true.

Nov 29th, 2014
HelloWorld
Category:
Statistics
Price: $5 USD

Question description

A sportswriter wished to see if a football filled with helium travels farther, on average, than a football filled with air. To test this, the writer used 18 adult male volunteers. These volunteers were randomly divided into two groups of nine subjects each. Group 1 kicked a football filled with helium to the recommended pressure. Group 2 kicked a football filled with air to the recommended pressure. The mean yardage for Group 1 was  = 30 yards with a standard deviation s1 = 8 yards. The mean yardage for Group 2 was  = 26 yards with a standard deviation s2 = 6 yards. Assume that the two groups of kicks are independent. Let μ1and μ2 represent the mean yardage we would observe for the entire population represented by the volunteers if all members of this population kicked, respectively, a helium-filled football and an air-filled football. Let σ1 and σ2 be the corresponding population standard deviations.

Based on the confidence interval for the difference in means and the test for equality of the standard deviations, we can draw a conclusion about the distribution of the lengths of the kicks with the two different kinds of footballs. Determine which of the following statements is true.

A.

The standard deviations of the air and helium groups seem to be the same. However, the means seem to be different.

B.

Both the means and standard deviations of the air and helium groups seem to be the same.

C.

The means of the air and helium groups seem to be the same. However, the standard deviations seem to be different.

D.

Both the means and standard deviations of the air and helium groups seem to be different from one another.


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