Stats Class, Wk 6

La Tonya Brooks
Wk 6
Stat Problem Set

Chap. 3

Ex. 88

  A. Mean: 73.06
        Mode: 66.20
        Std: 34.23

  B. Mean: 28
      Mode: 18
      Std: 26

  C. Mean: 45913
      Mode: 44174
      Std: 5894

Chap. 5

Ex. 56

A. p^n
0.9^4 = 0.6561

B. (1-p)^n
(1-0.9)^4
0.1^4
= 0.0001

C. at least one = 1 – prob(all arrived)
= 1 - 0.6561
= 0.3439

Chap. 6

Ex. 64

A. 0.270670566473225
 
B. = 1 - 4 or less
= 1 - 0.947346982656289
= 0.052653017343711

C. 0.135335283236613

Chap. 7

Ex. 50

A. z(65200) = (65200-60000)/2000 = 2.6
prob(z > 2.6)
= 0.466%

B. z(57060) = (57060-60000)/2000 = -1.47
z(58280) = (58280-60000)/2000 = -0.86
prob(-1.47 < z < -0.86)
= 12.41%
 

C. z(62000) = (62000-60000)/2000 = 1
prob(z < 1)
= 84.13%

D. z(70000) = (70000-60000)/2000 = 5
prob(z > 5)
= about 0% (it's greater than 0, but the z table shows it as 0)
It is not reasonable, since the proportion of a population that's more than 5 standard deviations above the mean is basically 0.

Chap. 8

Ex. 38

A. z = (25-23.5)/(5/sqrt(50))
z = 2.12132
prob(z > 2.12132)
= 0.0169

B. z(22.5) = (22.5-23.5)/(5/sqrt(50)) = -1.4142
prob(-1.4142 < z < 2.12132)
= 0.9044

C. z = +/-1.6449
The interval goes from:
mean - z*sd/sqrt(N) to mean + z*sd/sqrt(N)
23.5 - 1.6449*5/sqrt(50) to 23.5 + 1.6449*5/sqrt(50)
22.3369 to 24.6631

Chap. 9

Ex. 54

A. The t value for df = n-1 = 19, with 90% confidence is:
1.7291
The interval goes from:
mean - t*sd/sqrt(N) to mean + t*sd/sqrt(N)
10979 - 1.7291*1000/sqrt(20) to 10979 - 1.7291*1000/sqrt(20)
 

B. The z value for 99% confidence is 2.5758
The formula for sample size is:
N = (z*sd/E)^2
N = (2.5758*1000/250)^2
N = 106.16
Round up to:
N = 107

Chap. 10

Ex. 42
H0: game length is >= 3.5 hours
Ha: game length is < 3.5 hours
 
mean = 2.9553
stdev = 0.5596
 
Get the t test statistic:
t = (x-mu)/(stdev/sqrt(N))
t = (2.9553-3.5)/(0.5596/sqrt(17))
t =...