Question

Paired sample test, (1) construct a 95% confidence interval and (2) conduct a t-test (α = 5%). This is to report to the NFL commisioner regarding points scored vs points allowed.

Data sets below

Team	Points Scored	Points Allowed
Los Angeles	463	429
Seattle	452	271
Indianapolis	439	247
New Orleans	435	398
NY Gants	422	314
Cincinnati	421	350
San Diego	418	312
Philadelphia	410	388
Kansas City	403	325
Tennessee	399	421
Green Bay	398	344
Denver	395	258
Carolina	391	259
Pittsburg	389	258
New England	379	338
Buffalo	371	367
Minnesota	366	344
Houston	365	431
Jacksonville	361	269
Washington	359	293
Atlanta	351	341
Arizona	342	387
Dallas	325	308
Miami	318	317
Tampa Bay	300	274
Oakland	290	383
Baltimore	265	299
Chicago	260	202
Detroit	254	345
NY Jets	240	355
San Francisco	239	228
Cleveland	232	301

Answer 1

Team	Points Scored	Points Allowed	Difference(d)
Los Angeles	463	429	34
Seattle	452	271	181
Indianapolis	439	247	192
New Orleans	435	398	37
NY Gants	422	314	108
Cincinnati	421	350	71
San Diego	418	312	106
Philadelphia	410	388	22
Kansas City	403	325	78
Tennessee	399	421	-22
Green Bay	398	344	54
Denver	395	258	137
Carolina	391	259	132
Pittsburg	389	258	131
New England	379	338	41
Buffalo	371	367	4
Minnesota	366	344	22
Houston	365	431	-66
Jacksonville	361	269	92
Washington	359	293	66
Atlanta	351	341	10
Arizona	342	387	-45
Dallas	325	308	17
Miami	318	317	1
Tampa Bay	300	274	26
Oakland	290	383	-93
Baltimore	265	299	-34
Chicago	260	202	58
Detroit	254	345	-91
NY Jets	240	355	-115
San Francisco	239	228	11
Cleveland	232	301	-69
		Total	1096

Sample size = n = 32

Sample mean = = 34.25

Standard deviation = Sd = 77.850

Level of confidence interval is 0.95

Formula for confidence interval is

Degrees of freedom = n - 1 = 32 - 1 = 31

tc = 2.040 ( Using t table)