Statistics and Probability Answers

A rural community has two television stations, and on Saturday night the local viewers watch either the ‘Saturday Movie’ or the ‘Magic Show’. The following transition matrix contains the probabilities of a viewers watching one of the shows in a week, given that she had watched a particular show the preceding week.

This week Next week

Movie Magic

Movie 0.75 0.25

Magic 0.45 0.55

a) Given that a local viewer watched ‘Magic Show’ this week, use a decision tree to determine the probability that she will watch ‘Saturday Movie’ in week 4.

b) Determine the steady state probabilities.

c) If the community contains 1200 television sets, how many will turned to each show in the long run?

d) If a prospective local sponsor wanted to pay for commercial time on one of the shows, which show would more likely be selected? Explain.

a least squares regression to simulated data. Because we constructed these data using a​ computer, we know the SRM holds and we know the parameters of the model. We chose β0=7​, β1=0.5​, and σε=1.4. The fit is to a sample of n=50 cases. Use these results to complete parts​ (a) through​ (c) below.

​(a) If β1=0.5 in the​ population, then why​ isn't b1=0.5​?

​(b) Do the 95​% confidence intervals for β0 and β1 ​"work" in this​ example? (By​ "work," we mean that these intervals contain β0 and β1​, ​respectively.)

(c) What's going to change in this summary if we increase the sample size from n=50 to n=5,000​?

The following output summarizes the results of fitting a least-squares regression to simulated data. Because we constructed these data using a computer, we know the SRM holds and we know the parameters of the model. We chose Beta0 = 7, Beta1 = 0.5, and se = 1.5. The fit is to a sample of n = 50 cases

· If Beta1 = ½ in the population, then why isn’t b1 = ½?

· Do the 95% confidence intervals for Beta0 and Beta1 contain Beta0 and Beta1 in this example?

· What’s going to change in this summary if we increase the sample size from 50 cases to 5,000 cases?

East Texas Seasonings is preparing to build one processing center to serve its four sources of seasonings. The four source locations are at coordinates shown below. Also, the volume from each source is provided. What is the center of gravity?

X-coordinate

Y-coordinate

Volume

Athens, Texas

30

30

150

Beaumont, Texas

20

10

350

Carthage, Texas

10

70

100

Denton, Texas

50

50

400

A clothing chain is considering two different locations for a new retail outlet. They have identified the four factors listed in the following table as the basis for evaluation and have assigned weights as shown. The manager has rated each location on each factor, on a 100-point basis, as shown under the respective columns for Barclay and Chester.

Factor

Factor Description

Weight

Barclay

Chester

1

Average community income

0.40

30

20

2

Community growth potential

0.25

40

30

3

Availability of public transportation

0.15

20

20

4

Labor cost

0.20

10

30

Identify which location suitable for his new retail outlet.

4. The first product took 10 hours to build and the learning curve is estimated to be 90%. How long will it take to make the eighth unit?

T_N = T₁C

5. The first unit of production took 10 hours with a 90% learning curve. How long will it take to complete both the first and second units?

T_N = T₁C

1. A job with a 90% learning curve required 20 hours for the initial unit. The eighth unit should require approximately how many hours?

T_N = T₁C

2. A job requires 20 hours for the initial unit and 12.8 hours for the fourth unit. What is the learning rate?

T_N = T₁C

3. A job with a 95% learning curve required 19 hours for the second unit. The first unit should require approximately how many hours?

T_N = T₁C

The following output summarizes the results of fitting a least-squares regression to simulated data. Because we constructed these data using a computer, we know the SRM holds and we know the parameters of the model. We chose Beta0 = 7, Beta1 = 0.5, and se = 1.5. The fit is to a sample of n = 50 cases.

• If Beta1 = ½ in the population, then why isn’t b1 = ½?
• Do the 95% confidence intervals for Beta0 and Beta1 contain Beta0 and Beta1 in this example?
• What’s going to change in this summary if we increase the sample size from 50 cases to 5,000 cases?

the number of bank robberies that occur in Lagos is modeled to be poisson distribution with mean of 1.8 per day. find the probability of getting exactly three robberies in a day

The relationship between age (X, in year) and the number of overseas holidays a year (Y) has been studied using simple linear regression sing the following model.

Yi = 0 + 1 Xi + ui

The following table shows the data of age and the number of overseas destinations for a random sample of 20 respondents.

Age (X)

62

57

40

49

67

54

43

65

54

41

No of overseas holiday (Y)

6

5

4

3

5

5

2

6

3

1

Age (X)

44

48

55

60

59

63

69

40

38

52

No of overseas holiday (Y)

3

2

4

5

4

5

4

2

1

3

The summary of the data is as follows where SST is the total sum of squares, SSR is the regression sum of squares.

Xi = 1060, Yi = 73, Xi2 = 57994, Yi2 = 311, XiYi = 4097,

SST = Σ(𝑌𝑖−𝑌̅)2 = 44.55, SSR = Σ(𝑌̂𝑖−𝑌̅)2 = 28.65

a) Find the estimated regression line 𝑌̂𝑖 = b0 + b1 Xi that links the age with the number of overseas holidays in a year.

b) Test whether coefficient b1 is statistically significant or not. Use 5% significant level.

c) Interpret the estimated slope coefficient, b1.

d) Suppose that Ah Huat is 50 years old, predict how many times he has gone overseas for a holiday?

e) Give one quantitative and one qualitative variable that are expected to affect the number of overseas holiday in a year.