Question

Check My Work

The National Football League (NFL) polls fans to develop a rating for each football game. Each game is rated on a scale from 0 (forgettable) to 100 (memorable). The fan ratings for a random sample of 12 games follow. 57 61 85 74 72 72 20 58 79 78 84 74 a. Develop a point estimate of mean fan rating for the population of NFL games (to 2 decimals). b. Develop a point estimate of the standard deviation for the population of NFL games (to 4 decimals)

Answer 1

Solution:

We know that the sample mean Xbar is a point estimate of the population mean µ and sample standard deviation S is a point estimate of the population standard deviation σ.

Calculation table for finding mean and standard deviation for given data is summarised below:

No.	X	(X - Xbar)	(X - Xbar)^2
1	57	-10.8333	117.3603889
2	61	-6.8333	46.69398889
3	85	17.1667	294.6955889
4	74	6.1667	38.02818889
5	72	4.1667	17.36138889
6	72	4.1667	17.36138889
7	20	-47.8333	2288.024589
8	58	-9.8333	96.69378889
9	79	11.1667	124.6951889
10	78	10.1667	103.3617889
11	84	16.1667	261.3621889
12	74	6.1667	38.02818889
Total	814		3443.666667
Mean	67.8333

n = 12

Part a

Xbar = ∑X/n = 814/12 = 67.8333

A point estimate for mean fan rating for the population of NFL games is given as 67.83.

Part b

S = sqrt[∑(X - Xbar)^2/(n – 1)]

S = sqrt[3443.666667/(12 – 1)]

S = sqrt(3443.666667/11)

S = sqrt(313.0606061)

S = 17.69351876

A point estimate of the standard deviation for the population of NFL games is given as 17.6935.