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

Use the following information regarding a variable (Y) and a
variable (X) to answer the next 7 questions.
n =
8
∑ x = 56
∑ y = 296
∑ x 2 = 428
∑ y 2 = 11,920
∑ xy = 2,257
The sample covariance equals
26.43
-9.17
9.17
12.12
3 points
QUESTION 23
Refer to above data.
The sample correlation coefficient equals:
a.
-0.94
b.
1.67
c.
.991
d.
.85
3 points
QUESTION 24
Given the...

The authors of a paper presented a correlation analysis to
investigate the relationship between maximal lactate level
x and muscular endurance y. The accompanying data
was read from a plot in the paper.
x
410
740
770
790
850
1035
1210
1240
1290
1390
1475
1480
1505
2200
y
3.80
3.90
4.80
5.30
3.90
3.40
6.40
6.88
7.55
4.95
7.90
4.45
6.50
8.90
Sxx = 2,619,073.214, Syy
= 39.4021, Sxy = 7632.018. A scatter plot shows
a linear pattern.
(a)...

The following observations are obtained from a random sample of
10 individuals: Individual x y 1 9.08 5.25 2 4.23 3.58 3 6.88 4.75
4 10.3 5.38 5 8.09 4.27 6 10.6 5.79 7 4.50 3.41 8 8.32 5.75 9 7.17
4.74 10 9.45 5.43 Run a t-linear regression test on this data.
(HINT: make sure you copy the numbers correctly!) What are the
appropriate null and alternative hypotheses? H0:r=0H1:r≠0
H0:ρ=0H1:ρ<0 H0:ρ=0H1:ρ≠0 H0:r=0H1:r>0 H0:r=0H1:r<0
H0:ρ=0H1:ρ>0 What is the correlation coefficient?...

The authors of a paper presented a correlation analysis to
investigate the relationship between maximal lactate level
x and muscular endurance y. The accompanying data
was read from a plot in the paper.
x
400
760
770
810
850
1035
1210
1260
1290
1410
1475
1480
1505
2200
y
3.80
4.10
4.80
5.30
3.90
3.40
6.40
6.88
7.55
4.95
7.70
4.45
6.70
8.90
Sxx = 2,614,773.214, Syy
= 38.2727, Sxy = 7544.396. A scatter plot shows
a linear pattern.
(a)...

1. You are given the following data to fit a simple linear
regression x 1 2 3 4 5 y -2 4 2 -1 0 Using linear least squares,
determine the t-value for testing the hypothesis that no linear
relationship exist between y and x. (a) 0.01, (b) 0.03, (c) 0.09,
(d) 0.11, (e) 0.13

A world wide fast food chain decided to carry out an experiment
to assess the influence of advertising expenditure (A) on sales (S)
or vice versa. The table shows, for 8 randomly selected countries,
percentage increase in advertisement expenditure (A) and percentage
increase in sales (B) collected. The data presented in the
following table are the sums and sum of squares. (use 2 digits
after decimal point)
∑ A = 22.5 ∑ A2 = 64.91 ∑ ( A-Abar )2 =...

VERY URGENT
A world wide fast food chain decided to carry out an experiment
to assess the influence of advertising expenditure (A) on sales (S)
or vice versa. The table shows, for 8 randomly selected
countries, percentage increase in advertisement
expenditure (A) and percentage increase in sales (B)
collected. The data presented in the following table are
the sums and sum of squares. (use 2 digits after decimal
point)
∑ A = 22.5
∑ A2 = 64.91
∑ ( A-Abar )2...

Consider the data.
xi
2
6
9
13
20
yi
5
16
8
24
23
(a)
What is the value of the standard error of the estimate? (Round
your answer to three decimal places.)
(b)
Test for a significant relationship by using the t
test. Use α = 0.05.
State the null and alternative hypotheses.
H0: β0 ≠ 0
Ha: β0 = 0
H0: β1 ≠ 0
Ha: β1 =
0
H0: β1 = 0
Ha: β1 ≠ 0
H0:...

Consider the data.
xi
1
2
3
4
5
yi
2
8
6
11
13
(a)
Compute the mean square error using
equation s2 = MSE =
SSE
n −
2
. (Round your answer to two decimal places.)
(b)
Compute the standard error of the estimate using equation
s =
MSE
=
SSE
n −
2
. (Round your answer to three decimal places.)
(c)
Compute the estimated standard deviation of
b1
using equation
sb1 =
s
Σ(xi −
x)2...

Annual high temperatures in a certain location have been tracked
for a sample of 8 years. Let X represent the year and Y the high
temperature (in C∘).
x
y
5
33.06
6
30.48
7
27.2
8
24.42
9
22.34
10
17.96
11
16.38
12
13.8
Calculate the correlation coefficient. (Round to three
decimal places.)
r=
Let's test the significance of the correlation
coefficient at α=0.01 significance level.
H0: There is not a significant relationship between the year and
high...

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