(1) nominal: categorically discrete data without order the data For example: different person\'s name ordinal: quantities with order the data For example: rating scales interval:like ordinal and have interval between each value are equally split For example: temperature ratio levels: interval data with a natural zero point For example: time ------------------------------------------------------------------------------------------------------------ (2)population: is a group of phenomena sample is a part of the population parameter: is a characteristic of a population statistic: is a characteristic of a sample Advantages of Sample Surveys compared with Censuses: Reduces cost ------------------------------------------------------------------------------------------------------------ (3)Ordinal ------------------------------------------------------------------------------------------------------------ (4)Random ------------------------------------------------------------------------------------------------------------ (5) Given X~Binomial(n=9, p=0.53) P(X=x)=xC9*(0.53^x)*((1-0.53)^(9-x)) So the probability is P(X=3) =3C9*(0.53^3)*((1-0.53)^(9-3)) =0.1348013 Answer: 0.135 ------------------------------------------------------------------------------------------------------------ (6) Given X~Binomial(n=10, p=0.5) P(X=x)=xC10*(0.5^x) So the probability is P(X>=6)=P(X=6)+P(X=7)+...+P(X=10) = 0.3769531 Answer: 0.377 ------------------------------------------------------------------------------------------------------------ (7) P(X<0.285) = P((X-mean)/s <(0.285-0.3)/0.01) =P(Z<-1.5) =0.0668 (from standard normal table) Answer: 0.0668 ------------------------------------------------------------------------------------------------------------ (8) P(xbar> 215) = P((xbar-mean)/(s/vn) >(215-200)/(50/sqrt(40))) =P(Z>1.9) =0.0287 Answer: 0.0287 ------------------------------------------------------------------------------------------------------------ (9) r=-0.2 ------------------------------------------------------------------------------------------------------------ (10)4.88 + 0.525x ------------------------------------------------------------------------------------------------------------ (11)True ------------------------------------------------------------------------------------------------------------ (12) False ------------------------------------------------------------------------------------------------------------ (13) p=52/250 = 0.208 So the margin of error =Z*sqrt(p*(1-p)/n) =1.96*sqrt(0.208*(1-0.208)/250) =0.05031301 ------------------------------------------------------------------------------------------------------------ (14) n=(Z/E)^2*p*(1-p) =(1.645/0.04)^2*0.75*0.25 =317.1123 ------------------------------------------------------------------------------------------------------------ (15) n=(Z*s/E)^2 =(1.96*124/4.5)^2 = 2916.96 Take n= 2917 ---------------------------------------------------------------------------------------------------.

1. (1) nominal: categorically discrete data without order the data
For example: different person's name
ordinal: quantities with order the data
For example: rating scales
interval:like ordinal and have interval between each value are equally split
For example: temperature
ratio levels: interval data with a natural zero point
For example: time
------------------------------------------------------------------------------------------------------------
(2)population: is a group of phenomena
sample is a part of the population
parameter: is a characteristic of a population
statistic: is a characteristic of a sample
Advantages of Sample Surveys compared with Censuses: Reduces cost

2. ------------------------------------------------------------------------------------------------------------
(3)Ordinal
------------------------------------------------------------------------------------------------------------
(4)Random
------------------------------------------------------------------------------------------------------------
(5) Given X~Binomial(n=9, p=0.53)
P(X=x)=xC9*(0.53^x)*((1-0.53)^(9-x))
So the probability is
P(X=3) =3C9*(0.53^3)*((1-0.53)^(9-3)) =0.1348013
Answer: 0.135
------------------------------------------------------------------------------------------------------------
(6) Given X~Binomial(n=10, p=0.5)
P(X=x)=xC10*(0.5^x)
So the probability is
P(X>=6)=P(X=6)+P(X=7)+...+P(X=10) = 0.3769531
Answer: 0.377

3. ------------------------------------------------------------------------------------------------------------
(7) P(X<0.285) = P((X-mean)/s <(0.285-0.3)/0.01)
=P(Z<-1.5) =0.0668 (from standard normal table)
Answer: 0.0668
------------------------------------------------------------------------------------------------------------
(8) P(xbar> 215) = P((xbar-mean)/(s/vn) >(215-200)/(50/sqrt(40)))
=P(Z>1.9) =0.0287
Answer: 0.0287
------------------------------------------------------------------------------------------------------------
(9) r=-0.2
------------------------------------------------------------------------------------------------------------
(10)4.88 + 0.525x
------------------------------------------------------------------------------------------------------------
(11)True
------------------------------------------------------------------------------------------------------------
(12) False

4. ------------------------------------------------------------------------------------------------------------
(13) p=52/250 = 0.208
So the margin of error =Z*sqrt(p*(1-p)/n)
=1.96*sqrt(0.208*(1-0.208)/250)
=0.05031301
------------------------------------------------------------------------------------------------------------
(14) n=(Z/E)^2*p*(1-p)
=(1.645/0.04)^2*0.75*0.25
=317.1123
------------------------------------------------------------------------------------------------------------
(15) n=(Z*s/E)^2
=(1.96*124/4.5)^2
= 2916.96
Take n= 2917
------------------------------------------------------------------------------------------------------------
(16) p=293/1101 =0.2661217
So 95% confidence interval is

5. p +/- Z*sqrt(p*(1-p)/n)
--> 0.2661217 +/- 1.96*sqrt(0.2661217*(1-0.2661217)/1101)
--> (0.2400172, 0.2922262)
Answer: .240 < proportion < .292
------------------------------------------------------------------------------------------------------------
(17)False
------------------------------------------------------------------------------------------------------------
(18)margin of error E = t*s/vn =1.972*600/sqrt(190)
=85.83835
------------------------------------------------------------------------------------------------------------
(19) n=(Z/E)^2*p*(1-p)
=(1.96/0.05)^2*0.79*(1-0.79)
= 254.9286
------------------------------------------------------------------------------------------------------------
(20)the margin of error =t*s/vn = 2.074*8.2/sqrt(23) = 3.546163

6. Solution
(1) nominal: categorically discrete data without order the data
For example: different person's name
ordinal: quantities with order the data
For example: rating scales
interval:like ordinal and have interval between each value are equally split
For example: temperature
ratio levels: interval data with a natural zero point
For example: time
------------------------------------------------------------------------------------------------------------
(2)population: is a group of phenomena
sample is a part of the population
parameter: is a characteristic of a population
statistic: is a characteristic of a sample

7. Advantages of Sample Surveys compared with Censuses: Reduces cost
------------------------------------------------------------------------------------------------------------
(3)Ordinal
------------------------------------------------------------------------------------------------------------
(4)Random
------------------------------------------------------------------------------------------------------------
(5) Given X~Binomial(n=9, p=0.53)
P(X=x)=xC9*(0.53^x)*((1-0.53)^(9-x))
So the probability is
P(X=3) =3C9*(0.53^3)*((1-0.53)^(9-3)) =0.1348013
Answer: 0.135
------------------------------------------------------------------------------------------------------------
(6) Given X~Binomial(n=10, p=0.5)
P(X=x)=xC10*(0.5^x)
So the probability is
P(X>=6)=P(X=6)+P(X=7)+...+P(X=10) = 0.3769531

8. Answer: 0.377
------------------------------------------------------------------------------------------------------------
(7) P(X<0.285) = P((X-mean)/s <(0.285-0.3)/0.01)
=P(Z<-1.5) =0.0668 (from standard normal table)
Answer: 0.0668
------------------------------------------------------------------------------------------------------------
(8) P(xbar> 215) = P((xbar-mean)/(s/vn) >(215-200)/(50/sqrt(40)))
=P(Z>1.9) =0.0287
Answer: 0.0287
------------------------------------------------------------------------------------------------------------
(9) r=-0.2
------------------------------------------------------------------------------------------------------------
(10)4.88 + 0.525x
------------------------------------------------------------------------------------------------------------
(11)True

9. ------------------------------------------------------------------------------------------------------------
(12) False
------------------------------------------------------------------------------------------------------------
(13) p=52/250 = 0.208
So the margin of error =Z*sqrt(p*(1-p)/n)
=1.96*sqrt(0.208*(1-0.208)/250)
=0.05031301
------------------------------------------------------------------------------------------------------------
(14) n=(Z/E)^2*p*(1-p)
=(1.645/0.04)^2*0.75*0.25
=317.1123
------------------------------------------------------------------------------------------------------------
(15) n=(Z*s/E)^2
=(1.96*124/4.5)^2
= 2916.96
Take n= 2917
------------------------------------------------------------------------------------------------------------
(16) p=293/1101 =0.2661217

10. So 95% confidence interval is
p +/- Z*sqrt(p*(1-p)/n)
--> 0.2661217 +/- 1.96*sqrt(0.2661217*(1-0.2661217)/1101)
--> (0.2400172, 0.2922262)
Answer: .240 < proportion < .292
------------------------------------------------------------------------------------------------------------
(17)False
------------------------------------------------------------------------------------------------------------
(18)margin of error E = t*s/vn =1.972*600/sqrt(190)
=85.83835
------------------------------------------------------------------------------------------------------------
(19) n=(Z/E)^2*p*(1-p)
=(1.96/0.05)^2*0.79*(1-0.79)
= 254.9286

11. ------------------------------------------------------------------------------------------------------------
(20)the margin of error =t*s/vn = 2.074*8.2/sqrt(23) = 3.546163