Question

Home vs Road Wins – Significance Test: For the NHL regular season, the Chicago Blackhawks won 26 out of 41 home games and won 18 out of 41 away games. Clearly the Blackhawks won a greater proportion of home games. Here we investigate whether or not they did significantly better at home than on the road. The table summarizes the relevant data. The p̂'s are actually population proportions but you should treat them as sample proportions. The standard error (SE) is given to save calculation time if you are not using software.

Data Summary

	number of	total number	Proportion of
Game Type	wins (x)	of games (n)	wins (p̂)
Home	26	41	0.63415
Road	18	41	0.43902

SE = 0.11014

The Test: Test the claim that the proportion of wins at home was significantly greater than on the road. Use a 0.05 significance level.

(a) Letting p̂₁ be the proportion of wins at home and p̂₂ be the proportion of wins on the road, calculate the test statistic using software or the formula

z =

(p̂₁ − p̂₂) − δ_p

SE

where δ_p is the hypothesized difference in proportions from the null hypothesis and the standard error (SE) given with the data. Round your answer to 2 decimal places.
z =
To account for hand calculations -vs- software, your answer must be within 0.01 of the true answer.

(b) Use software or the z-table to get the P-value of the test statistic. Round to 4 decimal places.
P-value =

(c) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    

(d) Choose the appropriate concluding statement.

The data supports the claim that the proportion of wins at home was significantly greater than on the road.

While the proportion of wins at home was greater than on the road, the difference was not great enough to be considered significant.   

We have proven that the Blackhawks always do better at home games.

We have proven there was no difference in the proportion of wins at home than wins on the road.

Answer 1

(a)

H0: Null Hypothesis: p1 p2 ( the proportion of wins at home was not significantly greater than on the road. )

HA:Alternative Hypothesis: p1 > p2 ( the proportion of wins at home was significantly greater than on the road. ) (Claim)

n1 = 41

1 =26/41 = 0.63415

n2 = 41

2 = 15/41 = 0.43902

Pooled Proportion is given by:

Test Statistic is given by:

Z = 1.77

(b)

By Technology, Cumulative Area Under Standard Normal Curve = 0.9618

p value = 1 - 0.9618 = 0.0382

p value = 0.0382

(c)

Correct option:

reject H0

(d)

Correct option:

The data supports the claim that the proportion of wins at home was significantly greater than on the road.