Study of Relationship Between Hours Spent by Students Studying for a Test and their Scores

Introduction and Sampling 

In this project, 2 variables X and Y are required, X representing the hours spent by 11 students studying and Y representing the test scores that were attained by the 11 students. This data was obtained from the study textbook, and it shows how long it would take for a student to study for a test and the score they would get upon studying within that time. It is an interesting topic of discussion because it will help me as a student to relate for how long it will take me to study if I need certain scores on my test. However, some factors are not considered here, such as the level of concentration for the student. The population of interest here is students, who are preparing for a test, and their scores upon completion of the test. In the data collection, an interview was conducted for 11 students, who spent different hours studying for the test and their results differed. However, there are some cases whose hours of study were similar and the results obtained differed. 

Data 

Table 1. below illustrates the data collected on a survey of 11 students who were studying for a test and their scores together with the hours they spent studying recorded. With the two variables, X and Y, and a population of 11 students, the data is as follows; 

Hours spent studying (X)	0	2	3	4	5	5	5	6	7	8	13
Scores for the test (Y)	40	51	59	64	69	73	75	93	90	95	80

Table 1 hours spent studying and scores for the test 

All the data needed for this sampling has been clearly shown in the table. 

Descriptive Statistics 

In this section, the mean, mode and standard deviation of the data will be calculated. I did the calculations using an excel spreadsheet, but I will highlight the formulas used in the calculation for all and an explanation of what each parameter indicates. The respective graphical formulations and elaboration of each will be done under this section. The table 2 below shows the mean, mode and standard deviations for both variables, that is X, hours spent studying and Y, scores for the test. 

	MEAN	MODE	STANDARD DEVIATION
hrs spent studying	5.272727	5	3.408545
scores for test	71.72727	#N/A	17.53334

Table 2 mean, mode and standard deviation 

Mean is an average of all the values, where all the numbers are added up and divided by the total tally of the numbers. That is  . Mean is calculated to show the central tendency of a variable ( Livingston, 2004) . In our case, the central tendency for the hours spent studying lies at 5.27, while the scores for test lies at 71.72. This means that most of the students spent at least 5 hours studying, while the score that was achieved by most of the students was within 71. 

Mode is used to measure the average that can be used with nominal data. It is a measure of how frequent a variance has been repeated ( Livingston, 2004) . In our two variances, the hours spent studying has a mode of 5, whose frequency has been repeated 3 times, while in the scores for the test there is no mode. To find the mode, I have basically done tallying, putting similar numbers in one tally and coming up with the mode. 

Standard Deviation is a degree of the disparity of the data from the average value. A small value of standard deviation means the data is closer to the average value, and a big value of standard deviation signifies that the data is spread out in a wide range of values ( Livingston, 2004) . To formulate this, we square root the variance of the values. Variance is the average of the differences from the average value squared, hence the standard deviation ( Livingston, 2004) is calculated through the following formula;  . 

The graphical representation of the data is shown in the graphs below; 

graph 1 scatter graph showing test scores against studying hours 

graph 2 line graph showing test score against studying hours 

Confidence Intervals 

Using a 95% confidence interval, my margin of error will be 1.96 ( Hopkins, 2017) , hence the standard error for the test scores will be  = 10.36 

Therefore, the limits of the confidence interval can be obtained as follows; 

Lower limit = 71.72 – 10.36 = 61.36 

Upper Limit = 71.72+ 10.36 = 82.08 

Therefore, the range of the test score Mean at a 95% confidence interval will lie between 61.36 and 82.08. 

The standard error for the hours spent in studying using a 95% confidence interval will be  = 2 

The upper and lower limits will, therefore, be as follows; 

Lower Limit = 5.27 – 2 = 3.27 

Upper Limit = 5.27 + 2 = 7.27 

The range of the hours spent studying mean at a 95% confidence interval, for them to get that score will, therefore, be between 3.27 and 7.27. 

These are the values within which the correct value of the test score lies, and for the hours specified, the students who study for those hours have the highest chances of attaining those scores. 

Hypothesis Testing using the P-Value at 5% significance level, 

Null hypothesis:  H 0 :  ρ  = 0 

Alternate hypothesis:  H a :  ρ  ≠ 0 

The Z value is 2.20, therefore from our P-value from the P-statistic table is 0.0244 

Conclusion; we discard the null hypothesis, implying that, it is evident enough to come to an agreement that there exist a main linear link amid the  hours that students spent studying and test scores they obtained, since the coefficient of correlation significantly differs from zero. 

Conclusion 

From the above study, it is evident that there is an affirmative relationship between the hours spent by students studying for the test and the scores of the test studied for forming our data sample. These results can, therefore, be used to evaluate the efficiency of the reading hours if one wants to score a certain grade or marks. However, the level of ( Barbarick., & Ippolito, 2003) concentration and understanding for the students will also have an effect on their scores. Another factor that will influence the score for a test of a student is the state of the test, that is if it is within the student's ability to interpret. Nevertheless, how much content that the student will study within a certain number of hours and understand will also determine the scores for a student. Therefore, this method of determining how much time a student will need to study to get a certain score is not 100% accurate, since this is determined by several other factors. 

References 

Barbarick, K. A., & Ippolito, J. A. (2003). Does the Number of Hours Studied Affect Exam Performance?  Journal of Natural Resources and Life Sciences Education ,  32 (1), 32-35. 

Livingston, E. H. (2004). The mean and standard deviation: what does it all mean?  Journal of Surgical Research ,  119 (2), 117-123. https://doi.org/10.1016/j.jss.2004.02.008 

Hopkins, W. G. (2017). A Spreadsheet for Deriving a Confidence Interval, Mechanistic Inference and Clinical Inference from a P-Value. Sportscience ,  21 .