2. Consider the following data:

x= 1, 2, 3, 4, 5

y =3, 2, 4, 6, 5

By hand, not using Matlab, and showing your work:

(a) Compute the correlation coefficient.

(b) Find the least-squares line.

(c) Find the standard deviation around the least-squares line.

The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 1600 voters in the town and found that 68% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is over 65% . Determine the P-value of the test statistic. Round your answer to four decimal places.

TABLE 4-8 (According to the record of the registrar's office at a state university, 35% of the students are freshman, 25% are sophomore, 16% are junior, and the rest are senior. Among the freshmen, sophomores, juniors, and seniors, the portion of students who live in the dormitory are, respectively, 80%, 60%, 30%, and 20%. ) 40. Referring to Table 4-8, what is the probability that a randomly selected student is a freshman who lives in a dormitory?

41. Referring to Table 4-8, what is the probability that a randomly selected student is a sophomore who does not live in a dormitory?

42. 130) Referring to Table 4-8, what is the probability that a randomly selected student is a junior who does not live in a dormitory?

43. Referring to Table 4-8, what is the probability that a randomly selected student is a junior or senior who lives in a dormitory?

44. Referring to Table 4-8, what percentage of the students live in a dormitory? 45. Referring to Table 4-8, what percentage of the students do not live in a dormitory?

46. Referring to Table 4-8, if a randomly selected student lives in the dormitory, what is the probability that the student is a freshman?

47. Referring to Table 4-8, if a randomly selected student does not live in the dormitory, what is the probability that the student is a junior or a senior?

Siberian Charter Adventures is an independent Canadian company focused on providing unique charter tours to Siberia. The company has averaged between 1,000 and 1,500 tourists per month, and the operations manager wants to develop a forecast model to aid in planning. The operations manager has provided you with historical tourist data for the 24 months in 2014 and 2015.

1. Download the accompanying data file (MGSC369_R6_A4_datafile) and prepare a set of forecasts for each of the following three methods. Please read the instructions in the Excel^TM file carefully before you begin. Note that the forecasts can be created using Microsoft Excel, and you should submit your spreadsheet with your assignment for grading

a) Three-month moving average

b) Exponential smoothing based on what you believe to be an appropriate alpha constant. Provide a brief justification

c) Trend-adjusted exponential smoothing based on what you believe to be appropriate alpha and beta constants. Provide a brief justification for your choices.

2. Complete the following error summary table of the three forecasts, and then comment on the results. Identify which forecast method you believe the company should adopt.

A psychologist wants to see if a certain company has fair hiring practices in an industry where 60% of the workers are men and 40% are women. She finds that the company has 55 women and 52 men. Test to see if these numbers are different from the industry numbers, and if so, how are they different? Use alpha = .05 and four steps. what is the critical value of the test statistic?

Michelle runs a bakery that sells two kinds of cookies. Michelle knows the bakery must make at least 10 and at most 48 trays of the Nutty Squirrels. The bakery must also make between 3 and 72 trays of the Chocolate Decadence. The trays of Nutty Squirrels take 9 ounces of flour, while trays of Chocolate Decadence require 8 ounces of flour. The bakery only has 864 ounces of flour available. If trays of Nutty Squirrels generate $1.82 in profit, and trays of Chocolate Decadence generate $2.54, how many trays of the cookies should Michelle have the bakery make to get the most profit?

Nutty Squirrels:
Chocolate Decadence:
Best profit:

Consider the following time series data. Week 1 2 3 4 5 6 Value 18 13 17 12 17 15 a. Which of the following is a correct time series plot for this data? What type of pattern exists in the data? b. Develop the three-week moving average forecasts for this time series. Compute MSE and a forecast for week (to 2 decimals if necessary). MSE The forecast for week c. Use to compute the exponential smoothing forecasts for the time series. Compute MSE and a forecast for week (to 2 decimals). MSE The forecast for week d. Compare the three-week moving average approach with the exponential smoothing approach using . Which appears to provide more accurate forecasts based on MSE? e. Use a smoothing constant of to compute the MSE (to 2 decimals). Does a smoothing constant of or appear to provide more accurate forecasts based on MSE? The exponential smoothing forecast using provides a forecast than the exponential smoothing forecast using since it has a smaller MSE.

Apply the requirements, rules, or recommendations that can guide organizations into successful implementations of embedded analytics by selecting a case study from your own work environment.

Which test is used when looking at comparison of means from a single dependent variable among two or more groups or samples?

The accompanying data show the number of people working and the sales for a small bookstore. The regression line is given below. The bookstore decides to have a gala event in an attempt to drum up business. They hire 103 employees for the day and bring in a total of $ 41,000.

Sales = 7.873 + 0.946(Number of Salespeople Working)

Number of Salespeople Working // Sales

2 // 9

3 // 12

7 // 14

9 // 14

10 // 17

10 // 20

12 // 20

16 // 23

16 // 22

22 // 29

x (overline) = 10.7

y (overline) = 18.0

SD(x) = 6.13

SD(y) = 5.96

Complete parts a through d below.

a) Find the regression line predicting Sales from Number of people working with the new point added.

b) What has changed from the original regression​ equation? ​

c) Is the new point a high leverage point or an influential​ point? ​

d) Does the new point have a large​ residual? .

Let (X1, X2) have a bivariate normal distribution with mean vector (µ1, µ2), variance σ 1² for X1 and σ 2 ² for X2 and correlation cor(X1, X2) = ρ.

(a) Write down the joint density f(x1, x2).

(b) Find the marginal distribution f(x1)

(c) Find the conditional distribution f(x1 | x2) and the mean and variance of the conditional distribution.

(d) Obtain the likelihood equations and calculate the MLE for µ1, µ2, σ1² , σ2 ² , ρ.

In 2001​, a reproductive clinic reported 43 live births to 169 women under the age of​ 38, but only 9 live births for 75 clients aged 38 and older. Is there evidence of a difference in the effectiveness of the​ clinic's methods for older​ women? Determine the test statistic, the p-value, and if there is a difference, estimate the difference p1-p2 with a 95% confidence interval.

Community members who attended the Annual Neighborhood picnic earlier today are experiencing illness which they believe are related to food served at the picnic. Using the table below:

Calculate the attack rate for the 1) baked ham, 2) spinach, and 3) cabbage salad. Show your work.

Which food (of the baked ham, spinach, and cabbage salad) is MOST LIKELY to have caused the illness? Discuss your answer.