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PowerPoint Presentation STT100 Statistics for Business WEEK 7/8 Assignment Instructions and Help Hypothesis Testing THIS IS AN INDIVIDUAL ASSIGNMENT DUE FRIDAY WEEK 10 1500 words As a document Must have bibliography HOW TO DO THE ASSIGNMENT STEP BY STEP Tri 1 2019 Assignment Based on Research and Hypothesis Testing This assignment requires you to select a topic of interest which can be examined using available statistics about a population. Decide if your topic will be investigated using either a (option 1) Proportion or a (option 2) Mean You then are required to collect data on a sample of a population concerning your selected topic of interest. You are then to conduct a hypothesis test to find out if the sample is similar or significantly different to the population. This means that you compare if the sample mean is equal to or not equal to the population mean or if the sample proportion is equal or not equal to the population proportion. You are also required to then conclude and explain why or why not the sample and population results and the sample are similar or different. Where possible you should support your findings with journal articles on this topic. Does the sample have different characteristics for example to the population, are there differences that are social, cultural, economic, geographical or are there time differences between the two (for example different ages of the people in the sample, different era, etc). Explain the possibility of Type1 and Type 11 errors that you could have made when drawing your conclusion. This will be the most important part of your answer that makes your answer different and analytical ie why is your sample different to the population STEPS IN COMPLETING YOUR Individual ASSIGNMENT Examples of possible sample PROPORTIONS See other possible examples at the end of this section OPTION 1 1. An Example assignment ANSWER,using proportions Assignment Based on Research and Hypothesis Testing 1. This assignment requires you to select a topic of interest which can be examined using available statistics about a population. You then are required to collect data on a sample of a population concerning your selected topic of interest. You are then to conduct a hypothesis test to find out if the sample is similar or significantly different to the population. This means that you compare if the sample mean is equal to or not equal to the population mean or if the sample proportion is equal or not equal to the population proportion. You are also required to then conclude and explain why or why not the sample and population results and the sample are similar or different. Where possible you should support your findings with journal articles on this topic. Does the sample have different characteristics for example to the population, are there differences that are social, cultural, economic, geographical or are there time differences between the two (for example different ages of the people in the sample, different era, etc). Explain the possibility of type1 and Type 11 errors that you could have made when drawing your conclusion. 55% 5% 8% 2% 5% 55% of a normal population have BROWN eyes I will take a sample of students at PIA and calculate from this sample what proportion have BROWN eyes. I hypothesis that the PIA sample will be significantly different to the normal population You would include some information on this in the INTRODUCTION Other possible proportions to investigate for your own assignment…….. See other possibilities at the end of this step explanation BUT it will be best if you come up with your own original thing to investigate Assignment Based on Research and Hypothesis Testing 1. This assignment requires you to select a topic of interest which can be examined using available statistics about a population. 2. You then are required to collect data on a sample of a population concerning your selected topic of interest. You are then to conduct a hypothesis test to find out if the sample is similar or significantly different to the population. This means that you compare if the sample mean is equal to or not equal to the population mean or if the sample proportion is equal or not equal to the population proportion. You are also required to then conclude and explain why or why not the sample and population results and the sample are similar or different. Where possible you should support your findings with journal articles on this topic. Does the sample have different characteristics for example to the population, are there differences that are social, cultural, economic, geographical or are there time differences between the two (for example different ages of the people in the sample, different era, etc). Explain the possibility of type1 and Type 11 errors that you could have made when drawing your conclusion. I create a table and do a count of the different colours of the eyes of my sample students (10) selected from a sample of PIA students. StudentnationalityEye colour 1 2 3 4 5 6 7 8 9 10 Step 1 & 2 HERE YOU COLLECT YOUR SAMPLE DATA Assignment Based on Research and Hypothesis Testing This assignment requires you to select a topic of interest which can be examined using available statistics about a population. You then are required to collect data on a sample of a population concerning your selected topic of interest. 3. You are then to conduct a hypothesis test to find out if the sample is similar or significantly different to the population. This means that you compare if the sample mean is equal to or not equal to the population mean or if the sample proportion is equal or not equal to the population proportion. You are also required to then conclude and explain why or why not the sample and population results and the sample are similar or different. Where possible you should support your findings with journal articles on this topic. Does the sample have different characteristics for example to the population, are there differences that are social, cultural, economic, geographical or are there time differences between the two (for example different ages of the people in the sample, different era, etc). Explain the possibility of type1 and Type 11 errors that you could have made when drawing your conclusion. STEPS TO FOLLOW TO COMPLETE AN HYOTHESIS TEST STEPS: State the Null hypothesis (Ho )and the Alternative hypothesis (HA ). Choose the level of significance. All of you will choose 95%. Find the critical value. Since you are using a 95% level of significance, for a proportion this will be using ‘z‘ =1.96 (see the z table) and for a sample mean this will be using ‘t‘ and a sample of 10 t= 1.833 (see the t table) . Find the test statistic. You do this using the formulae= Draw a conclusion. If your test statistic is greater than the critical value reject the null, your sample is different to the population (recommended). The null is that the sample and the population are the same. The Alternative is that they are different You will have ‘rigged’ the data so that your sample is DIFFERENT STEPS TO FOLLOW TO COMPLETE AN HYPOTHESIS TEST 1. The null hypothesis Ho is what you believe to be true and is always Ho = Eg That the sample mean from your experiment is equal to the population mean That means the two are the same. In this case the sample proportion will be the same as the population proportion…NOTE we have rigid this not to be the case The alternative hypothesis is what you claim to be or believe to be, Ha or H1. The null hypothesis can be: Ha ≠ 0 Ha > 0… this is a one tail test In this case the sample proportion will NOT be the same as the population proportion…NOTE we have rigid this to be the case 2. The level of significance is generally always 5% or 0.05.. Thus we are testing whether the sample and population are greater than 95% DIFFERENT 3. Find the critical value = 1.645 for one tail Ha > 0 or 1.960 for two tails Ha ≠ 0 STEPS: State the Null hypothesis (Ho )and the Alternative hypothesis (HA ). Choose the level of significance. All of you will choose 95%. Find the critical value. Since you are using a 95% level of significance, for a proportion this will be using ‘z‘ =1.96 (see the z table) and for a sample mean this will be using ‘t‘ and a sample of 10 t= 1.833 (see the t table) . Find the test statistic. You do this using the formulae= Draw a conclusion. If your test statistic is greater than the critical value reject the null, your sample is different to the population (recommended). STEPS TO FOLLOW TO COMPLETE AN HYOTHESIS TEST 4. Find the test statistic Use the following to calculate the test statistic Population proportion Sample proportion Population proportion Sample size 1 -Population proportion 5. Draw conclusions Null Hypothesis ZONE Accept H0 If test statistic in this zone That is your answer to the equation is LESS than 1.645 Alternative Hypothesis ZONE Reject H0 If test statistic in this zone That is your answer to the equation is GREATER than 1.645 1.645 STEPS: State the Null hypothesis (Ho )and the Alternative hypothesis (HA ). Choose the level of significance. All of you will choose 95%. Find the critical value. Since you are using a 95% level of significance, for a proportion this will be using ‘z‘ =1.96 (see the z table) and for a sample mean this will be using ‘t‘ and a sample of 10 t= 1.833 (see the t table) . Find the test statistic. You do this using the formulae= Draw a conclusion. If your test statistic is greater than the critical value reject the null, your sample is different to the population (recommended). STEPS TO FOLLOW TO COMPLETE AN HYOTHESIS TEST EXAMPLE CALCULATION: Assume the sample proportion of brown eyes is 90% or 0.9 and the population proportion of brown eyes is 55% 0r 0.55 Use the following to calculate the test statistic Population proportion Sample proportion Population proportion Sample size 1 -Population proportion 5. Draw conclusions Null Hypothesis ZONE Accept H0 If test statistic in this zone That is your answer to the equation is LESS than 1.645 Alternative Hypothesis ZONE Reject H0 If test statistic in this zone That is your answer to the equation is GREATER than 1.645 1.645 Z = Z = Z = Z = Z= 2.2247 Z= 2.2247 So reject the null and conclude that the sample is significantly different to the