Question 1

The distance Y necessary for stopping a vehicle is a function of the speed x of the vehicle. Suppose the following set of datawere observed for 12 vehicles travelling at different speeds as shown in the table below.

Vehicle No. Speed, kph Stopping Distance, m

1 40 15

2 9 2

3 100 40

4 50 15

5 15 4

6 65 25

7 25 5

8 60 25

9 95 30

10 65 24

11 30 8

12 125 45

(a) Plot the stopping distance versus the speed of travel.

(b) Assume that the stopping distance is a linear function of the speed, i.e. Y = a + bx + e .

Estimate the regression coefficients, a and b, and the standard deviationsY/x. Also,

determine the correlationcoefficient between Y and x.

(c) Determine the 90% confidence intervalof the regression equation based on Xi = 9, 30,

60 and 125.

Question 2

The actual concrete strength Y in a structure is generally higher than that measured on a

specimen, x, from the same batch of concrete. Data show that a regression equation for

predicting the actual concrete strength is:

Y = 1.12x + 0.05 (ksi); 0.1 < x < 0.5

and Var(Y ) = 0.0025 (ksi)2

Assume that Y follows a normal distributionfor a given value of x.

(a) For a given job, in which the measured strength is 0.35 ksi, what is the probabilitythat

the actual strength will exceed the requirement of 0.3 ksi?

(b) Suppose the engineer has lost the data on the measured strength of the concrete

specimen. However, he recalls that it is either 0.35 or 0.40 with the relative likelihood of

1 to 4. What is the probability that the actual strength will exceed the requirement of 0.3

ksi?

(c) Suppose the measured values of concrete strength at two sites A and B are 0.35 and 0.4

ksi, respectively. What is the probability that the actual strength for the concrete

structure at site A will be higher than that at site B? You may assume that the predicted

actual concrete strength between the sites is statistically independent.

Question 3

Experienced flight instructors have claimed that praise for an unexceptionally fine landing is

typically followed by a poor landing on the next attempt, whereas criticism of a faulty

landing is typically followed by an improved landing. Should we thus conclude that verbal

praise tends to lower performance while verbal criticism tends to raise them? Is some other

explanation possible?

Question1

a)

b) Results of the regression analysis conducted on the given data by using analysis tool of MS Excel is given below

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.9835

R Square 0.9672

Adjusted R Square 0.9640

Standard Error 2.6780

Observations 12.0000

ANOVA

df SS MS F

Regression 1.0000 2117.9510 2117.9510 295.3260

Residual 10.0000 71.7157 7.1716

Total 11.0000 2189.6667

Coefficients Standard Error t Stat P-value

Intercept -2.0108 1.4877 -1.3516 0.2063

Speed 0.3861 0.0225 17.1851 0.0000

Regression Equation Y = -2.0108 + 0.3861 X

Regression coefficients: a = -2.0108 and b = 0.3861

Standard Deviation

Correlation between Y and X = …

The expert plots the vehicle stopping distance versus the speed of travel.