Question

I. Solve the following problem:
For the following data:
1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 6 n = 12

b) Calculate
1) the average or average
2) quartile-1
3) quartile-2 or medium
4) quartile-3
5) Draw box diagram (Box & Wisker)

II. PROBABILITY

1. Answer the questions using the following contingency table, which collects the results of a study to 400 customers of a store where you want to analyze the payment method.

_______B__________BC_____
A 10 40
AC 180 170
_________________________

For the next questions assume that clients are selected randomly or randomly. Determine the probability that .....
a) P (A) b) P (A / B) c) P (A ∩ BC) d) P (BC / A)
e) P (A ∪ B) f) P (B ∩ BC)

2. An oil company purchased a land option in Alaska. Preliminary geological studies assign the following probabilities of finding oil. P (high quality oil) = 0.50, P (medium quality oil) = 0.20, P (non-oil) = 0.30 After drilling 200ft, a sample of the soil was taken that depth. The probabilities of finding oil in this type of soil are the following: P (special type of soil / high quality oil) = 0.20; P (special type of soil / medium quality oil) = 0.80; P (special type of soil / non-oil) = 0.20 Halle P (special soil type),

III. Discrete Distributions:
Binomial
1. A university learned that 8% of its students withdraw from the introductory course in statistics. Suppose that in this quarter 8 students enrolled in that course.
 a.What is the probability that two or less are unsubscribed?
 b.What is the expected number of students discharged?

Poisson
2. The passengers of the lines arrive randomly and independently to the documentation section at the airport, the average frequency of arrivals is 1.2 passengers per minute.
to. What is the probability of non-arrivals in a one-minute interval?
b. What is the probability that three or fewer passengers arrive in a two minute interval?

IV. Continuous Distribution: Normal

Normal
1. The average time to complete a final exam in a given course is normally distributed. With average of 80 min, and standard deviation of 8 minutes. For a certain student taken at random:
to. What is the probability of finishing the exam in an hour or less?
b. What is the probability of finishing the exam between 60 min and 70 min?

Exponential
2. The time to fail in hours of a laser beam in a cytometric machina can be modeled by an exponential distribution with λ = .00004

* What is the probability that a laser fails more than15000 hours?
* What is the probability that a laser fails less than 25000 hours?

V. Hypothesis test and confidence intervals.

1. A sample (n) is taken at random from a population and produces (the sample)
 A

= 1100, S = 200. Try the following hypothesis: If we assume the following size of
sample n = 36
a, Is there evidence that the average μx is less than 1200? α = .10

H0: μx = 1200
 H1: μx <1200

* For the previous test (item a) estimate the p-value
* Determine the power of the previous hypothesis test. (1-β)
* Estimate 95% confidence interval for the true average value.

SAW. Linear Regression and Correlation.

The following n = 5 data were collected for a linear regression study for two variables.

26 24 144 158 136
ΣX ΣY ΣXY ΣX ^ 2 ΣY ^ 2

_____ X Y
2 2
Four. Five
5 3
7 7
8 7

to. Develop a graph X, Y (Scatter diagram)
* Compute the linear regression equation
* If x = 10, what value would you estimate for "y" the linear regression equation?
* Test the following hypothesis for the previously calculated linear regression slope:
       Use an alpha of α = .10 MSE = 1.544
  
Ho: β = 0 There is no linear relationship between X and Y
Ha: β> 0 There is some positive linear relationship between X and Y

* Compute the correlation coefficient r
* Test the following hypothesis for the previously calculated correlation coefficient:
       Use an alpha of α = .01
  
Ho: ρ = 0 There is no relationship between X and Y
Ha: ρ> 0 There is some positive relationship between X and Y

* Compute the correlation coefficient r
* Test the following hypothesis for the previously calculated correlation coefficient:
       Use an alpha of α = .01
  
Ho: ρ = 0 There is no relationship between X and Y
Ha: ρ> 0 There is some positive relationship between X and Y

 VI1. Goodness of fit test for the Poisson distribution
We want to test the following hypothesis for a given study.

Ho The cars parked in the houses follow a Poisson distribution with λ = 1.3.
Ha Cars parked in houses Do not follow a Poisson distribution with λ = 1.3.

Use an α = .10 750 observations were taken. The data of a study are the following:

Number of cars Frequency   λ=1.3
                      P(x)
0 170                 .2725
1 270                 .3543
2 200                 .2303
3 o mas 110                 .1429

Answer 1

problem I

a)

mean = ΣX/n = 37.000/12.000=3.083

b)

quartile , Q1 = 0.25(n+1)th value=3.25th value of sorted data

=2

c)

Median=0.5(n+1)th value = 6.5th value of sorted data

=3.0000

d)

Quartile , Q3 = 0.75(n+1)th value=9.75th value of sorted data

=4

e)

problem II

	B	BC	total
A	10	40	50
AC	180	170	350
total	190	210	400

a)

P(A) = 50/400=0.1250

b)

P(A/B) = P(A n B)/P(B) = 10/190=0.0526

c)

P(A n BC) = 40/400=0.1000

d)

P(BC/A) = 40/50=0.8000

e)

P(A u B)=(180+10+40)/400=0.5750

f)

P(B n BC) = 0