Statistics for Business

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Unit Name (in full):Statistics for Business

Number of Questions: Part A: Central Tendency, Part B; Hypothesis Testing, Part C; Regression Analysis, and, Dummy Variables.

• This exam is worth 60 % of your mark for the unit.

• The 60 marks are distributed across all of the questions.

• You have until Sunday 10 pm 7th June evening to complete the exam.

• You will complete the exam by typing out your answers in a word file.

• Obviously, this is an individual examination, and you are asked to be honest and ethical in the execution of the task. 

• YOU RISK FAILING THE UNIT IF THE TURN IT IN SIMILARITY IS HIGH BUT ESPECIALLY IF IT IS 100%

• You will upload your completed paper to Moodle through the turn it in file designated on the STT 1000 Moodle page.

Question 1. Central tendency

Based on lecture notes provided

Use material from lecture ONE supplied with the email containing this exam to help find the answers.

Where you need to label you will need to use a text box!

Eg.

1. Distinguish between:

mean, median and mode.

2. When is a median a better measure of central tendency?

3. When is a mode a better measure of central tendency?

4. Use the numbers given below and the formulae and table provided to calculate:

The mean = …………

The variance = ……….

The standard deviation = ………….

Numbers: 10, 12, 15, 18, 21

Variance Formulae

S²

= the mean formulae

Standard Deviation Formulae

S

n	x		=
1	10		=
2	12		=
3	15		=
4	18		=
5	21		=

On the following normal curve:

1. Label the mean
2. Label 1 standard deviation either side of the mean as +1 SD and – 1 SD.
3. Shade and insert the percentage of the curve that is between +1 SD and – 1 SD from the mean.
4. What is the probability that a sample statistic will be in the region shaded?

5. “Z” scores are measured along the horizontal axis. What then does a Z score measure?
6. To calculate the z score we use the following formulae:

Where X = a sample value in the data set

= the sample mean

S = the sample standard deviation

If for this examination the mean mark is 60/100 and the Standard deviation is 10. You receive lets say a mark of 80/100.

1. Calculate the z score. Answer ……….
2. Use the normal curve below to find out what percentage of students will have a mark higher than your mark of 80/100

Answer ………

Question 2.

Hypothesis Testing based on lecture provided plus help notes for the Assignment

Use material from the lecture material supplied with the email containing this exam to help find the answers.

Where you need to label you will need to use a text box!

Eg.

1. Distinguish between:

1. A one tail and a 2 tail hypothesis test. (provide a diagram to illustrate)
2. A Null hypothesis and an alternative hypothesis (for the alternative there are 3 types include all)
3. A Type 1 error and a Type ii error when drawing conclusions from your hypothesis test.
4. On the following normal curve:

Write and locate for a TWO TAIL TEST each of the following:

1. The accept the null hypothesis zone.
2. The reject the null hypothesis zone.
3. The critical value cut off points.

Other questions on this curve:

4. If the level of significance is 5%, what is the critical value
5. If the test statistic calculated using one of the formulae asked for in the next part of this set of questions is 4.5.

Do you accept OR reject the null?

……………………………………………………………

3. Write out the formulae for the test statistic using:

1. The population and sample proportion.
2. The population mean and Standard deviation.

In the following you are to use the results from statistics concerning the number of children per woman per country to test whether the country given is significantly different to the average number of children per woman in the data set

The country that you are testing is NIGERIA

The results for the population that is all countries is below:

Questions

1. State the null and the alternative hypothesis
2. Use the following formulae to calculate the test statistic:

The Standard deviation for ALL countries read from the calculation from “calculatorsoup”

The NUMBER (count) of countries in the world whose data you have read from the calculation from “calculatorsoup”

The mean or average for the country you have selected

The mean or average for ALL countries read from the calculation from “calculatorsoup”

Z = ……………………………

3. Conclude whether this country is significantly higher or lower than the average number of children born per woman across all countries the data is provided for. Given that the critical values are:

+1.960

-1.960

Question 3.

Correlation and Dummy variables based on lecture provided.

Use material from the lecture material supplied with the email containing this exam to help find the answers.

Where you need to label you will need to use a text box!

Eg.

1. Distinguish between correlation and causation.
2. On the blank diagram below draw the regression line and add the labels asked for.

1. The x and y axis
2. The dependent variable and independent variable axis
3. A regression line that indicates that as the variable on the x axis increases the variable on the y axis increases. What is this relationship called?
4. Provide a real-world example of a relationship where, as the x variable (name this) increases the y variable also increases (name this).
5. Label the gradient and the slope of this regression line that you have drawn.

4. If the regression equation is y = 100 + 1.5 X

And X = 100 calculate the value of Y.

2. Explain the meaning of the 1.5 X.

4. Fully distinguish between: Define and give the value range.

1. R the coefficient of correlation
2. R² the coefficient of determination.

5. Give THREE features of a dummy variable:

i.

ii.

iii.

3. Give an example of a real-world dummy variable.
4. On the following diagram of a regression indicate the effect on the regression line if the dummy is present.

6. Distinguish by writing out the general formulae for each between:

1. A simple regression and
2. A multiple regression

7. The following print out is called ANOVA Analysis of Variance.

A simple regression how investment affects GDP

A Multiple regression adding consumption to Investment to see the effect of both on GDP

1. Write out the multiple regression equation for this regression.
2. What statistic in the print-out will tell us if by adding the extra x variable if the predictive ability of our analysis has been improved?

8. Read and understand the information provided below:
9. Using this material consider the print-out of the regression above. Draw conclusions about the two x variables (Consumption and Investment) and indicate why you have come to that conclusion.

This is written in exponential notation:

4.65E-05 = 0.0000465 ie. move the decimal point 5 places to the left.

P-value… tests the null hypothesis that the coefficient is equal to zero (no effect) (0 would indicate that there is no relationship between X and Y).

A low p–value (< 0.05) indicates that you can reject the null hypothesis….and therefore accept the alternative that there is a relationship between X and Y Typically, you use the coefficient p–values to determine which terms to keep in the regression model. Reject variables where p-value is zero ie no effect

THE END OF THE EXAM

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