Does Peyton Manning have a greater
passing ability in domes? After all,
inside a dome the weather is always
nice for throwing the ball! The
accompanying relative frequency
histograms show Manning’s 18 career
road performances inside a dome and
his 86 career performances outside
(through the 2010 season). In this
case, his performance is measured
with his passer rating, a combination
or passing yards, completion
percentage, number of touchdowns,
and number of interceptions. Only
road games are included because
Manning plays his home games in a dome and the benefit of playing in a dome would be impossible to separate
from the benefit of playing at home.
a. Briefly compare these distributions.
b. State the hypotheses we are interested in testing.
c. Manning’s mean passer rating in domes was 109.3 and his mean passer rating outside was 89.8, for a
difference (dome – outside) of 19.5. Describe how to simulate the distribution of this test statistic, assuming
that Manning’s ability is the same in both locations.

d. Here are the results of 100 trials of the simulation from part c. Describe what information is provided by the
dotplot.
e. Use the dotplot to estimate and interpret the p-value.
f. Using the p-value from part e, make an appropriate conclusion.
g. Is there is convincing evidence that Manning had a greater ability in domes, can we conclude that the dome is
the cause? Explain.

did u ever get the answers for it lol. i need help on it too

Answer:

ok so i had this for my stat class and i came on here to try and figure it out but didn't find any answers, so i just went ahead and tried it for myself. i'm not sure if i'm 100% correct, so if anyone knows the right answers leave a comment / post the right answers

ALSO my stat teacher gave us this exact assignment with these exact pictures so if ur gonna use these answers make sure you paraphrase them/reword them as best as you can

a) Briefly compare these distributions.

The distribution of passing ability for Manning’s passes in domes is relatively symmetrical while the distribution of his passes outside is skewed to the left. The distribution of outside performances varies slightly more than that of his performances within domes; outside performances vary from about 40-160 while performances in domes vary from about 60-160 (passer ratings).

b) State the hypotheses we are interested in testing.

H(o): Peyton Manning does not have a greater passing ability in domes than outside.

H(a): Peyton Manning has a greater passing ability in domes than outside.

c) Manning’s mean passer rating in domes was 109.3 and his mean passer rating outside was 89.8, for a difference (dome – outside) of 19.5. Describe how to simulate the distribution of this test statistic, assuming that Manning’s ability is the same in both locations.

1. Using 104 note cards, write each deviation on a different note card.

2. Shuffle the cards and divide them into two groups; one for passes outside, and one for passes within a dome.

3. Calculate and record the simulated difference (dome - outside) in standard deviation for the two types of pitches.

4. Repeat many times.

d. Here are the results of 100 trials of the simulation from part c. Describe what information is provided by the dotplot.

The dotplot illustrates the simulation repeated 100 times, with each dot representing a difference between the difference (dome - outside) for each individual simulation.

e) Use the dotplot to estimate and interpret the p-value.

Because there are no dots greater than or equal to our previously calculated difference of 19.5, the p-value = 0/100 = 0.

f) Using the p-value from part e, make an appropriate conclusion.

Since it is impossible (p = 0) to have a difference (dome - outside) in observed standard deviations of 19.5 or more by random chance alone when the true standard deviation of Manning’s passes was the same inside and outside a dome, there is convincing evidence that the true standard deviation of Manning’s passes was greater for his passes in a dome than outside a dome.

g) If there is convincing evidence that Manning had a greater ability in domes, can we conclude that the dome is the cause? Explain.

We can never 100% conclude that the dome is the primary cause of his better performance within domes. Other things like wind, crowd cheering, motivation, and teamwork could be some of the various causes of his better performance.

Step-by-step explanation:

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