# Perform a statistical enquiry that will either prove or disapprove my hypothesis.

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Introduction

Statistical Enquiry Aim: To perform a statistical enquiry that will either prove or disapprove my hypothesis. Hypothesis: Higher the persons IQ, higher the SAT results Method: In this statistical enquiry, I aim to find out if people that have higher IQ have better results in English. For me to be able to perform the enquiry I had to have data about the IQ of students. I have a database of pupils of Mayfield High School, which is a fictional school based on data from real schools, complete with their IQ. Because it is based on real schools, the data will be reliable and accurate enough for me to draw a conclusion from the enquiry. There are 1183 pupils at Mayfield High School- I decided to compare 10% of general population. This is roughly 100 pupils. The hundred people I get from the general population will be my sample. Since there are different strata's in my data, I had to find out what number of boys or girls from each year group I am going to take from my hundred samples. For that I used stratified sampling. Stratified Sampling Students in Mayfield high school are the population of the school. The population of the school are the pupils that are being studied. Since in Mayfield High School there are 1183 pupils, it would be very impractical for me to study and compare all of the data. I have to take a sample- a smaller group of people from general population. I have decided to take 10% of general population as my sample. Year Group Number of boys Number of girls 7 151 131 8 145 125 9 118 143 10 106 94 11 84 86 In the Mayfield School database there are different strata's for the data. Strata are distinctive non-overlapping subsets of the population. In this case the data has been divided into the year groups of the population, then additionally by their gender.

Middle

Instead I do the group frequency of the IQ. Everything is done the same as for the main data. The only difference is that the data is much smaller. IQ Frequency 70-79 2 80-89 4 90-99 8 100-109 11 110-119 5 120-129 0 This table shows the frequency of the particular value in my data. As you can see there are several differences form my general sample data. For one thing, there I no student in years 10 and 11 that have IQ higher than 120. Also there is no very distinctive majority for any particular data. These differences can be shown by a frequency polygon. As you can see, the difference from the order frequency polygon is that it has broader width. The frequency of the IQ values is more disturbed between them. Frequency table of SAT results Since there aren't any large ranges of values, I am able to use normal frequency table for SAT results data. SAT levels Frequency 1 0 2 2 3 7 4 14 5 8 My frequency table, like that for the general data, shows that predominant level is level 4. However, as with the Y10 and 11 tables, the frequency of the values is more disturbed. This is the frequency polygon of the SAT results The frequency polygon shows the data in the table and illustrates the difference of distribution from the original sample frequency polygon. Mean of year 10 and 11 I need to do mean for IQ and SAT results. I used the same method as previously in obtaining the mean. I will try to see if it will match the means of the general sample data. Mean of IQ For my mean of IQ I decided to do the calculation of sum of values using Excel. It is faster and more convenient than doing it by hand. Mean = Sum of values/number of values Mean = 3166/31 Mean = 102.12 Mean is smaller than with the main data, but this could be because I used smaller number of data so there is less variety.

Conclusion

However, the reason why the correlation isn't any stronger is because there are many other factors which affect SAT results. While having IQ increases your chances, it isn't the only thing that affects if you get good grade. Factors such as amount of time spent studying or watching TV might also have an impact on what the grade a person gets. The hypothesis is true but there are many other things beside IQ that causes a high SAT grade. I did the summary statistic to see what the average is of the population of that particular school. The results I got such as correlation coefficient and regression line are only relative to the particular population that gets this kind of averages. It might be that this school isn't an average school in a country and that you will get a different results in other schools. While these results can be applied to this school, it is possible that they cannot be applied in different schools. Evaluation I performed a statistical enquiry using mathematical methods to improve or disapprove my hypothesis. I have completed my investigation successfully, proving my hypothesis. I used summary statistics in describing a population. I have calculated regression line and I have found out the correlation coefficient. This investigation was done thoroughly and accurately as I could possibly make it. I believe it was a success. However, I believe there are certain ways I could improve the investigation. I know that IQ affects SAT results, but now I could try to see what other factors also affect the results. I could perform an investigation to see if amount of time spent studying or watching TV has any effect on the SAT results. Also, I could see if this data could be applied to more schools than one. I could get a sample of schools from the entire country and see if there summary statistics match mine. I could find out if the Mayfield High School is an average school of the country. 1 Maja Jovanovski

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