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 0.01 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 formulaz =

(p̂1 − p̂2) − δp

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 H₀fail 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) The null and alternative hypothesis are:

; i.e., the the proportion of home wins and road wins for Chicago Blackhawks is not different.

; i.e., the the proportion of home wins for Chicago Blackhawks is greater than the road wins.

We need to test the hypothesis at the given significance level of

Test-statistic:

where,

; sample proportion of win in home

total number of home games.

sample proportion of win in road

total number of road games.

pooled proportion

Standard error is given in the question as SE= 0.11014

calculation for test-statistic:

The test-statistic is calculated as

(b) Since it is a right-tailed test, so the p-value is calculated as-

So, the p-value for the test-statistic is calculated as

(c) Conclusion:

Since,

(d) So at significance level the data does not provide enough evidence to support the alternative hypothesis H₁ . Hence "we conclude that the proportion of wins at Home and at Road for the Blackhaws is not significantly different or we can say based on sample data there is no significant difference in the wins at Home and at Road for Blackhawks."