Question

The mean throwing distance of a football for Marco, a high school freshman quarterback, is 40 yards, with a standard deviation of two yards. The team coach tells Marco to adjust his grip to get more distance. The coach records the distances for 20 throws. For the 20 throws, Marco’s mean distance was 45 yards. The coach thought the different grip helped Marco throw farther than 40 yards. Conduct a hypothesis test using a preset α = 0.05. Assume the throw distances for footballs are normal. First, determine what type of test this is, set up the hypothesis test, find p-value, Sketch the graph, and state your conclusion.

Answer 1

Solution:

Given: The mean throwing distance of a football for Marco, a high school freshman quarterback, is 40 yards, with a standard deviation of two yards. That is and

Sample size = n = 20

Sample mean =

Level of significance = α = 0.05

We have to test if  the different grip helped Marco throw farther than 40 yards.

that is: test if mean

Part a) what type of test this is?

We use z test, since  the throw distances for footballs are normal distribution with known standard deviation .

Part b) set up the hypothesis test.

Vs  

( Since H1 is > type, this is right tailed test)

Part c)  find p-value.

For right tailed test , p-value is:

p-value = P(Z > z test statistic)

Where

Thus

p-value = P(Z > 11.18)

p-value = 1 -  P(Z < 11.18)

Since z = 11.18 is more than z = 3.00, Area under the curve to left of z = 11.18 is approximately equal to 1

that is: P( Z< 11.18) = 1

thus

p-value = 1 -  P(Z < 11.18)

p-value = 1 - 1

p-value = 0.0000

Part d) Sketch the graph:

Part e) state your conclusion

Decision Rule:
Reject null hypothesis H0, if p-value < 0.05 level of significance, otherwise we fail to reject H0

Since p-value = 0.0000 < 0.05 level of significance, we reject null hypothesis H0.

Thus at 0.05 level of significance, we have sufficient evidence to conclude that:  the different grip helped Marco throw farther than 40 yards.