Question

A sports writer 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 eighteen 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 x¯1=300 yards with a standard deviation s1=8 yards. The mean yardage for Group 2 was x¯2=296 yards with a standard deviation s2=6 yards. Assume the two groups of kicks are independent. Let μ1 and 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- and air-filled football. Assuming two-sample t procedures are safe to use, a 90% confidence interval for μ1−μ2 is Select one:
(A) (1.5,9.5)
(B) (-1.9,9.9)
(C) (-5.9,13.9)
(D) (-3.7,11.7)

Answer 1

Answer:

(-3.07, 11.07)

Step-by-step explanation:

Given that a sports writer 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 eighteen adult male volunteers. These volunteers were randomly divided into two groups of nine subjects each.

Group   Group One     Group Two  

Mean 300.00 296.00

SD 8.00 6.00

SEM 2.67 2.00

N 9     9    

The mean of Group One minus Group Two equals 4.00

 

standard error of difference = 3.333

   df = 16

t = 1.2000

Margin of error = 3.3333* t critical = 3.3333*2.121

 95% confidence interval of this difference: From -3.07 to 11.07