Respuesta :
Answer:
a. The estimate of mean fan rating for the population of NFL games=68.08
b. The estimate of standard deviation=18.8785
Step-by-step explanation:
Given
The fan ratings for a random sample of 12 games follow:
57, 61, 87,74,72,73,19,56,81,79,83 and 75
a.Mean =[tex] \frac{ sum\;of\;data}{ total\;number \; of data}[/tex]
Mean=[tex]\frac{57+61+87+74+72+73+19+56+81+79+83+75}{12}[/tex]
Mean= 68.08
b.[tex]\mid x-\bar x\mid[/tex] [tex]{\mid x-\bar x\mid}^2[/tex]
11.08 122.7664
7.08 50.1264
18.92 357.9664
5.92 35.0464
3.92 15.3664
4.92 72.6192
49.08 2408.8464
12.08 145.9264
12.92 166.9264
10.92 119.2464
14.92 734.064
6.92 47.8864
Standard deviation=[tex]{\sqrt\frac{\sum{\mid x-\bar x\mid}^2}{n}[/tex]
n=12
[tex]\sum{\mid x-\bar x\mid}^2=4276.7872[/tex]
Standard deviation=[tex]\sqrt\frac{4276.7872}{12}[/tex]
Standard deviation=[tex]\sqrt{356.3989}[/tex]
Standard deviation = 18.8785
The estimate of the standard deviation for the population of NFL games=18.8785
The point estimates for the mean and standard deviation of the given data is respectively; 68 and 17.6
What is point Estimate?
A) To find the point estimate of the mean, we add all up all the data and divide by the number of values.
Thus;
∑x = 57 + 61 + 86 + 87 + 72 + 73 + 19 + 56 + 81 + 79 + 83 + 75 = 816
n = 12 numbers
Thus;
mean = ∑x/n = 816/12
Mean = 68
B) To find the estimate of the standard deviation, we would get it from the formula;
s = √[(n*(∑x²) - (∑x)²)/n(n - 1)]
∑x² = 572 + 612 + 862 + ... + 742 = 59,010
s = √[ (12*(59,010) - (816)²)/(12)(11)]
s = 17.6
Read more about Point Estimate at; https://brainly.com/question/9562180
