# Statistics for Business Essay Example

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Mathematics
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200032 Statistics for Business Autumn 2011

 School of Computing and Mathematics College of Health and Science ## Assignment

Autumn 2011

ID Number Name

 Group Member 1 Group Member 2 Group Member 3 Group Member 4

Tutorial time: __________________________________________

Variable (assigned in class):
1.Average UAI 2.Annual Total Cost 3.Average Indebtedness

1. The file named “Assignment Data Set”, containing the data sets for the following questions, can be downloaded from the e-learning site vUWS.

1. You should use Excel to carry out all calculations and statistical analyses. To get started with Excel, see the instructions on page 13 of the textbook.

1. To complete this assignment, you must provide the Excel outputs for each of the questions in a report.

1. Your assignment submitted must be typed and word-processed.

1. The maximum number of pages for each submission is three (3), not including the cover page. No mark will be given if the number of pages exceeds the limit.

1. Part 1 of the assignment is to be submitted in Week 7 in your tutorial class while Part 2 of the assignment is to be submitted in Week 13 in your tutorial class.

1. Any late assignments will be penalised 10% of the total mark per day

A study was commissioned to investigate universities in America. Data was collected on 80 universities and the following variables recorded.

School Number

Type of Term 2 semesters =1, 4 terms = 0

Location City = 1, Suburban = 2, Country = 3

Type of School Private = 1, Public = 0

Average UAI Average University Admissions Index

Enrolment Number of students enrolled

Annual Total Cost Annual total cost of attending (\$’000)

Average Indebtedness Average indebtedness at graduation (\$‘000)

#### For questions 1 and 2, use the variable assigned

Question 1 (1 + 1 + 1 + 1 = 4 marks)

Find the a) mean,

b) Median,

c) Range and

d) Standard deviation of your variable.

Question 2 (1 + 1 = 2 marks)

a) Construct a frequency distribution for your variable using 6 classes.

b) Display this frequency distribution as a histogram Question 3 (2 + 1 + 1 = 4 marks)

Consider the following events concerning a university chosen at random

A University selected is a private university i.e. Type of School = 1

B University selected has 2 semesters i.e. Type of Term = 1

a) Find the number of universities in each of the following categories.

1. A university is selected at random. Find P (A|B).

P (A|B) = 50/59

1. Are A and B statistically independent?

The event A and B are statistically independent

## Question 5 (2 marks)

Estimate with 95% confidence the average annual total cost.

 Annual Total Cost 2.049875 Standard Error 0.065889122 Standard Deviation 0.589330222 Sample Variance 0.347310111 Kurtosis -1.390029309 Skewness -0.167390019 Confidence Level(95.0%) 0.131149014

## Question 6 (2 marks)

Using an appropriate hypothesis test, can we conclude that the data provide evidence that the average enrolment is greater than 500?

 Average Enrolment Standard Error 14.31919548 Standard Deviation 128.0747779 Sample Variance 16403.14873 Kurtosis -1.072138943 Skewness -0.005245661 Confidence Level(95.0%) 28.50164517

## Question 7 (3 marks)

Using an appropriate hypothesis test, can you show if there is any difference between the annual total cost of public and private universities and colleges?

## Question 8 (1 + 2 = 3 marks)

1. Estimate the regression equation to predict the Annual Total cost (y) from the Average indebtedness (x).

1. Does the data provide evidence that the slope of the equation from part a) is positive? Perform an appropriate hypothesis test.

Annual Total cost (y) = 1.278 + 0.0588 Average indebtedness (x): R2 = 0.424

This implies that Annual total cost is positively related with Average indebtedness, the higher the annual indebtedness, the higher the annul cost and vice versa. However, Annual indebtedness is not a good predictor of annual cost since R2 = 0.424

NOTE: The data was randomly created for the sole purpose of this assignment.