Two sample tests on means

Recall that when comparing two means, we must first decide if the two variables are dependent (or paired) vs if they are independent

1. Using the hockey data, test if the true mean number of wins is greater than the true mean number of losses, using a significance level of 0.01. (Note that both cases just refer to the W and L columns, nothing fancier.)

2. Using the hockey data, test if the actual average goal differential between the Eastern Conference is different from that of the Western Conference, using a significance level of 0.05.

Team	Conference	Division	W	L	OTL	Pts	GF	GA	Diff
Tampa Bay	Eastern	Atlantic	55	17	10	120	284	230	54
Boston	Eastern	Atlantic	55	17	10	120	270	205	65
Toronto	Eastern	Atlantic	57	16	9	123	298	214	84
Florida	Eastern	Atlantic	45	23	14	104	254	249	5
Detroit	Eastern	Atlantic	30	38	14	74	226	248	-22
Montreal	Eastern	Atlantic	30	44	8	68	213	267	-54
Ottawa	Eastern	Atlantic	25	45	12	62	222	289	-67
Buffalo	Eastern	Atlantic	26	50	6	58	191	286	-95
Washington	Eastern	Metropolitan	51	21	10	112	249	244	5
Pittsburgh	Eastern	Metropolitan	49	25	8	106	275	248	27
Philadelphia	Eastern	Metropolitan	47	29	6	100	263	246	17
Columbus	Eastern	Metropolitan	49	28	5	103	225	222	3
New Jersey	Eastern	Metropolitan	43	30	9	95	263	254	9
Carolina	Eastern	Metropolitan	24	45	13	61	243	259	-16
NY Islanders	Eastern	Metropolitan	42	27	13	97	263	304	-41
NY Rangers	Eastern	Metropolitan	37	35	10	84	207	254	-47
Nashville	Western	Central	53	21	8	114	272	221	51
Winnipeg	Western	Central	46	23	13	105	286	221	65
Minnesota	Western	Central	32	36	14	78	246	229	17
Colorado	Western	Central	43	29	10	96	271	242	29
St Louis	Western	Central	51	25	6	108	223	238	-15
Dallas	Western	Central	37	34	11	85	235	230	5
Chicago	Western	Central	32	39	11	75	217	253	-36
Vegas	Western	Central	52	20	10	114	261	224	37
Anaheim	Western	Pacific	42	30	10	94	228	213	15
San Jose	Western	Pacific	44	27	11	99	244	228	16
Los Angeles	Western	Pacific	44	27	11	99	233	191	42
Calgary	Western	Pacific	38	34	10	86	215	243	-28
Edmonton	Western	Pacific	34	36	12	80	250	268	-18
Vancouver	Western	Pacific	23	48	11	57	213	266	-53
Arizona	Western	Pacific	32	37	13	77	209	253	-44

Calculate the test statistic (Round answer to 2 decimal places) Calculate the p-value (Round answer to 4 decimal places) This test statistic leads to a decision to

• accept the null
• fail to reject the null
• reject the null

Provide Explanation with : 1. Hypotheses :

2. Assumption check:

3. Decision rule:

4. Descriptive statistics:

5. Decision:

6. Conclusion:

Sample just like below

Hypotheses:

H0: 0.44

H1: < 0.44

Assumption check:

1) "Success" does come from a binomial distribution.

2) 0=350(.44) = 154 5 3) 0=350(.66) = 196 5 Thus, we can employ the central limit theory that says the distribution of is approximately normal and inferences on the actual proportion of counties which are considered inside a metro area should be valid.

Decision rule:

If the p-value is less than the pre-determined alpha of 0.01, we will reject the null hypothesis.

Descriptive statistics:

= 0.3829

z = -2.15

p-value = 0.0156

Decision:

Because the p-value of 0.0156 is greater than the pre-determined alpha of 0.01, we fail to reject the null hypothesis.

Conclusion :

We can not conclude that the actual proportion of counties that are considered inside a metro area was less than 44%