# Statistics of One Variable

I have attached several problems that I need solved.

Questions - u4

The questions are to be answered with full solutions. Be sure to focus on proper mathematical form, including:

1. One equal sign per line,

2. Equal signs in each question lined up vertically with each other,

3. No self-developed short form notations.

4. One step or idea per line,

5. Show complete solution to the given problem.

________________________________________

1. The following distribution gives the numbers of hours of overtime during one month for the employees of a company:

Overtime (h) 0 1 2 3 4 5 6 7 8 9 10

Employees 10 2 4 2 6 4 2 4 6 2 8

Display the data in a histogram.

2. The numbers of service calls a heating company made during the first ten days of November are listed below. Find the mean, median and mode for this set of data.

6, 28, 28, 11, 30, 21, 17, 28, 28, 20

3. The mean of the values 9, 11, 13, 21, 24, 18 and d is 17. Find the value of d. Show the steps you followed to solve for d.

5. When recommending five investments for you to consider, your financial planner mentions that the typical minimum investment is $2 000 since the minimum investment amounts for the five funds being considered are: $500, $2 000, $2 500, $25 000 and $ 2000 respectively. However, when you key these numbers into a calculator, you find the average minimum investments is in fact $6 400. What a accounts for this discrepancy?

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#### Solution Summary

This provides examples of working with statistics, including displaying data, central tendency, and quartiles.

Business Statistics

Please answer all questions. Please show all your work (detailed solution) so i can understand how you came up with the anwer. Thanks

(See attached file for full problem description)

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EXHIBIT 1: A manager at a local bank analyzed the relationship between monthly salary and three independent variables: length of service (measured in months), gender (0=female, 1=male) and job type (0=clerical, 1=technical). The following tables summarizes the regression results:

df SS MS F

Regression SS 3 1004346.771 334782.257 5.96

Unexplained SS 26 1461134.596 56197.48445

Coefficients Standard Error t Stat P-Value

Constant 784.92 322.25 2.44 0.02

Service 9.19 3.20 2.87 0.01

Gender 222.78 89.00 2.50 0.02

Job -28.21 89.61 -0.31 0.76

(1) Referencing Exhibit 1, based on the SS table and 0.05 significance level, the global null hypothesis test of the multiple regression model (2 points):

(a) Will be rejected and conclude that monthly salary is related to all the independent variables

(b) Will be rejected and conclude that monthly salary is related to at least one of the independent variables

(c) Will not be rejected

(d) Will show a high multiple coefficient of determination

(e) Cannot be ascertained given the above information ______________

(2) Referencing Exhibit 1, the adjusted multiple coefficient of determination is (3 points):

(a) 5.93%

(b) 59.3 %

(c) 40.7 %

(d) 33.9%

(e) None of the above ________________

(3) Referencing Exhibit 1, based on hypothesis tests for the individual regression coefficients at a 5% significance level (2 points),

(a) All the regression coefficients are not equal to zero,

(b) "Job" is the only significant independent variable in the model

(c) Only "Service" and "Gender" are significantly related to monthly salary

(d) "Service" is the only significant variable in the model

(e) None of the variables are significant ________________

(4) Referencing Exhibit 1, which of the variables are dummy variables in the model (2 points)?

(a) Salary

(b) Service

(c) Service and gender

(d) Gender and job

(e) Service, gender and job ________________

(5) Referencing Exhibit 1, the results for the variable "Gender" show (2 points)

(a) Males average $222.78 more than females in monthly salary

(b) Females average $222.78 more than males in monthly salary

(c) Gender is not related to monthly salary

(d) Gender and months of service are correlated ________________

(6) A survey of 144 retail stores revealed that a particular brand and model of a VCR retails for $375 with a standard deviation of $20. What is a 99% confidence interval to estimate the true cost of the VCR?

_____________________

(7) A survey of an urban university (population 25,450) showed that 870 of 1100 students sampled supported a fee increase to fund improvements to the student recreation center. Using the 95% level of confidence, what is the confidence interval for the true proportion who support the fee increase?

_____________________

(8)The average cost of tuition, room and board at small private liberal arts colleges is reported to be $8,500 per term but a financial administrator believes that the average cost is higher. A study conducted using 150 small liberal arts colleges showed that the average cost per term is $9,000 with a standard deviation of $1,200. What is the decision at 0.05 level of significance?

_____________________

(9) The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights are recorded as 9.0; 7.3; 6.0; 8.8; 6.8; 8.4; and 6.6 pounds. What is the decision for a statistical significant change in average weights at birth at the 5% level of significance?

_____________________

(10) A manufacturer of automobile transmissions uses three different processes. The management ordered a study of the production costs to see if there is a difference among the three processes. A summary of the findings is shown below.

Process 1 Process 2 Process 3

Process Totals ($ 100's) 137 108 107

Sample Size 10 10 10

Sum of Squares 1893 1188 1175

What is the sum of squares for treatments?

_____________________

For problem 10, what is the sum of squares for error?

_____________________

For problem 10, what is your conclusion at alpha = .05?

_____________________

(11) A sales manager for an advertising agency believes there is a relationship between the number of contacts and the amount of sales. To verify this belief, the following data was collected:

Salesperson # of Contacts Sales ($ '000)

1 14 24

2 12 14

3 20 28

4 16 30

5 46 80

6 23 30

7 48 90

8 50 85

9 55 120

10 50 110

What is the value of coefficient of determination ?

_____________________

For problem 11, what is the regression equation?

_____________________

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(See attached file for full problem description)

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