Question

3. 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 18 adult male volunteers. These volunteers were randomly divided into two groups of nine men 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 vardage for Group 1 was "=300 yards with a standard deviation 1 8 yards. The mean yardage for Group 2 was = 296 yards with a standard deviation 9 6 yards. Assume the two groups of kicks are independent. Let A and 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 and an air-filled football. Assuming two-sample t procedures are cafe to use test versus . What do we conclude about the gas filling a football at a 10%? a. There is no evidence that there is a difference between helium-and air-filled footballs, on average. Ob. There is evidence that air-filled footballs go farther, on average. Oc. There is evidence that helium-filled footballs go farther, on average. 4. A researcher wished to compare the effect of two stepping heights (low and high) on heart rate in a step-aerobics workout. A collection of 50 adult volunteers was randomly divided into two groups of 25 subjects each. Group 1 did a standard step-aerobics workout at the low height. The mean heart rate at the end of the workout for the subjects in Group 1 was 1 = 90.00 beats per minute with a standard deviation of = 9 beats per minute. Group 2 did the same workout but at the high step height. The mean heart rate at the end of the workout for the subjects in Group 2 was = 95.08 beats per minute with a standard deviation of 2 - 12 beats per minute. Assume that two groups are Independent and the data are approximately Normal. Let and represent the mean heart rates we would observe for the entire population represented by the volunteers, if all members of this population did the workout using the low or high step height, respectively. Suppose the researcher had wished to test the hypotheses Holl y and The P-value for the test is (use conservative value for the degrees of freedom) a. between 0.05 and 0.01. Ob. between 0.10 and 0.05. Oc. larger than 0.10.

Answer 1

3)

Since the population standard deviations are not known, we use T-test.

a)Here, the sample means are
X1 = 300, X2 = 296
. The sample standard deviations are
S1 = 8, S2 = 6
. Also
6 = ºu = 'u
,
g = 0.1

The test statistic is

t = X1 - x2 nin2 0-296 t= += 1.2

The P-value is

P-value = P(T< -1.2) P-value = 0.1238034

Since , we accept the null hypothesis. There is no evidence to support there is a difference between the 2 footballs.

P-value = 0,12 g = 0,1

Correct choice (a).

We are required to solve only one question. Please post the remaining questions as another post.