Question

The following table shows the number of wins eight teams had during a football season. Also shown are the average points each team scored per game during the season. Construct a​ 90% prediction interval to estimate the number of wins for teams that scored an average of 27 points a game

Wins	13	7	3	9	3	7	11	8
Points per Game	25.5	18.5	20.3	24.5	12.2	22.5	22.9	23.6

Determine the upper and lower limits of the prediction interval.

UPL=

LPL=

Answer 1

SOLUTION :

From given data,

Construct a​ 90% prediction interval to estimate the number of wins for teams that scored an average of 27 points a game

Where ,

90% = 90 / 100 = 0.9

= 1-0.9

= 0.1

sample number = n =8

Wins	Points Per Game (X)
13	25.5	(25.5- 21.25)2 = 18.0625
7	18.5	(18.5- 21.25)2 = 7.5625
3	20.3	(20.3- 21.25)2 = 0.9025
9	24.5	(24.5- 21.25)2 = 10.5625
3	12.2	(12.2- 21.25)2=81.9025
7	22.5	(22.5- 21.25)2 = 1.5625
11	22.9	(22.9- 21.25)2 = 2.7225
8	23.6	(23.6- 21.25)2 = 5.5225

   = 170 = 128.8

Mean = = = 170/8

= 21.25

Variance= = =

= 128.8 / 7

= =18.4

Standard deviation ==  

= s = 4.289

Degree of freedom (df) = n-1 = 8-1 = 7

t_critical = t_,df = t_0.1,7 = 1.895 (for two tailed test)

Confidence interval

CI = /

= 21.25 1.895 4.289 /

= 21.25 1.8951.51639

= 21.25 2.87355

(21.25 - 2.87355 , 21.25 - 2.87355)

(18.3764 , 24.1235)

where,

UPL = 24.1235

LPL = 18.3764