STT100 Statistics for Business

NOTE AT FIRST THE STATISTICS SEEM TO MAKE THIS A DIFFICULKT TASK. BUT IF YOU FOLLOW THE GUIDE IT IN IN FACT STRAIGHT FORWARD.

STEP 1.

Select one of the areas of investigation

1. Number of children per woman per country
2. Use the following link : https://www.cia.gov/library/publications/the-world-factbook/rankorder/2127rank.html
3. Copy from the excel file the column “Median years” and past it into the following online Statistical tool to calculate the mean and standard deviation of the median ages of all countries;

http://www.calculatorsoup.com/calculators/statistics/descriptivestatistics.php

          Your result will look like this (with different numbers):..you will need the mean and standard deviation to complete the test statistic see later)

 Calculator soup uses the raw data and gives you numbers that you need to calculate your test statistic:

 This includes :

1. The average for all countries
2. The country with the highest value
3. The country with the lowest value
4. N -the sample size (The total number of countries0
5.  

• The standard deviation

For my data:

1. x¯average = 2.52892857143
2. Minimum min = 0.83
3. Maximum max = 6.49
4. n = 224
5. Standard Deviation s = 1.20507027288

1. Select a country with a number of children per woman

       either much HIGHER or Much Lower than the average. NOTE YOU COULD SELECT BOTH: -ONE COUNTRY THAT IS HIGH

   AND ONE THAT IS LOW

The aim of the assignment is to Conclude a hypothesis that STATISTICALLY the country selected is significantly higher or lower than the world average

STEP 2. Here you are drawing statistical conclusions about the selected country.

Conduct a Hypo thesis test using the following STEPS:

JUST COPY AND PASTE THIS INTO YOUR ANSWER

1. State the Null hypothesis (Ho) (it is not statistically different So H_o=0) and the Alternative hypothesis (HA) (it is statically different). H_a ≠ 0
2. Choose the level of significance. This either sets the normal range before the tails where it is not normal to be either 95% or 99% of the normal curve.
3. Find the critical value. This is the cut-off point on the normal curve in standard deviations between the Null (normal) not different and the alternative (in the tails of the normal curve) that it is significantly different. The critical value is found in statistical tables 95% =1.960 1.960 is the critical cut off value. YOU WILL ALL USE THIS
4. Find the test statistic. This calculated using ( A FORMULAE) with the X value for the country selected the average for all countries and the standard deviation using the data for all countries. The result of this calculation will be in standard deviations (Z Score) which will place the country selected in the normal range or the abnormal range of the normal curve. If the test statistic is < +1.960 or > -1.960 this country is normal & not significantly different to the average for all countries BUT IF the test statistic > 1.960 + then this country is significantly higher than the average for all countries And, if the test statistic is > 1.960 – then this country is significantly lower than the average for all countries

The normal curve below could be used to illustrate the cut off critical vales etc

could be used to

READ THE FOLLOWING BUT NO REAL NEED TO USE IT:

1. The null hypothesis H_o is what you believe to be true and is always H_o = the population average or proportion

The NULL HYPOTHESIS (H₀) is always equal to so H₀ = 0    Which means that we in the null are hypothesizing that the NOT significantly different to the average (number of children per woman in the data set)

The ALTERNATIVE HYPOTHESIS  (H_a) is either

                                                      * H_a ≠ 0 this means that the country selected is    

           (statistically significantly) different to the average number of children per Woman. This is a two tail test

YOU CAN SIMPLY ONLY DO THIS TEST IF YOU WANT!

BUT THERE ARE 2 OTHER POSSIBILITIES

• H_a> 0 this is a one tail test. It concludes whether the country that you select is significantly higher in terms of (in my case) that it has a statistically significantly higher number of children per woman than the average.
• H_a< 0  this is a one tail test. It concludes whether the country that you select is significantly LOWER in terms of  (in my case) that it has a statistically significantly LOWER number of children per woman than the average.

1. Choose the level of significance. ()

YOU WILL ALL select the same level of significance.

95% is what you will select. The only alternative is 99%

This means the following:

1. Find the critical value.

The critical value is measured in standard deviations from the mean (or the z score) where the cutoff point is between accepting the null or rejecting it and ( we do not say this but we accept the alternative)… This is found using the table above:

1. Find the test statistic.

                     This is found using a formulae:

The main one that you will use is:

x¯ = 2.52892857143

Minimum

min = 0.83

Maximum

max = 6.49

n =  224

Standard Deviation

s = 1.20507027288

STEP 3.

Draw a STATISTICAL CONCLUSIONS.

ONLY TWO CONCLUSIONS EXIST:

1. YES, this country is significantly statistically different to the average for all countries.
2. No, it is in the normal range and so it is NOT significantly statistically different to the average for all countries.

If Astra Seneca when it tested it Covid vaccine on a sample group of 3000 people it would give a placebo vaccine to 15000 and the real vaccine to the other 1500. Then it would use statistics to find if the group given the real vaccine hade significantly less symptoms of covid (maybe no symptoms) than the placebo group.

NOW DRAW CONCLUSIONS FROM THIS RESULT:                                                                                                                    

STEP 4.  

NOTE IT MIGHT BE EASIER TO SELECT A COUNTRY THAT IS HIGH OR LOW OF THE RANGE OF COUNTRIES FOR THEN THIS PART WILL BE EASIER TO FIND INFORMATION

Draw an ANALYTICAL CONCLUSIONS.

This is the part of the assignment is where you will gain the most marks.

IT INVOLVES SOME RESEARCH

Your, answer to this part will determine your MARK overall.

You must use referenced research to find out details about:

• WHY the country that you have considered is different (in the case above why is it not different) to the world average. What are the special reasons for this?
• What are the consequences and effects and costs (or benefits) for this country in having this difference or lack of difference?
• What government or social policies might be used to correct (or to cause this result) or have caused this difference or to benefit from this difference? Consider what other countries have done and make suggestions for this country based on what they have done.
• What other changes might this difference cause or what other changes might correct this difference? Why might it restrict this, countries?