# Free Statistics Research Paper Sample for You

Type of paper: Research Paper

Pages: 4

Words: 1100

Published: 2020/12/25

## Introduction

We all know that exercise brings great benefit to the lives of everyone. Playing sports, you strengthen your immune system, strengthen the muscles have a greater impact on cardiac system of the body. Due to physical exercise each person develops, reinforcing its character. Regular exercise is important for the health of men of any age - they protect from diseases and, as evidenced by various studies, slow the aging process. Exercise helps increase strength and endurance. Aerobics, cycling, tennis, basketball, jogging and skiing develop endurance, burning a lot of calories. They significantly strengthen the cardiovascular system, the foundation of good health. Exercises that produce power form the body and build muscle. Through the power of the body can be carried out a wide variety of actions that will get more out of life.
In this case study I would like to investigate the average time spent on sports by males and females and check if there is a significant difference in time spent on sport by gender.

## Data Gathering

For the purpose to gather the data I found a gym near my home and spent there a day. During all the day I asked each sportsman how many hours he or she spends on training per week (on average). I recorded the answer and the gender of respondent. That day there were 83 visitors in the gym. My sample consists of 83 observations.

## The Data

I’m given with the data of 83 observations of two variables:
Time – the number of hours spent in gym averagely per week.
Gender – the gender of respondent (0 – male, 1 – female).
The gathered data is in a table below:
Summarizing the Data
I begin with a descriptive statistics for hours spent on sport by the factor of gender. Descriptive statistics helps me to understand the distribution of the variables:

## Descriptive Statistics: Time

Variable Gender N N* Mean SE Mean StDev Minimum Q1 Median Q3
Time 0 46 0 6,761 0,561 3,808 1,000 3,000 6,500 10,000
1 37 0 6,919 0,567 3,451 1,000 4,500 7,000 9,500

## N for

Variable Gender Maximum Mode Mode
Time 0 13,000 3 5
1 13,000 6; 7; 8 5
According to the descriptive statistics the typical time spent on sports is 5 hours per week for both males and females (Mode = 5). The average time spent on sports is 6.761h for men and 6.919h for women. The men’s data is more dispersed than women’s (standard deviations are 3.808 and 3.451 respectively).

## Graphical visualization of the frequency distribution for each gender is given below:

Statistical Inference
In this section I will perform a hypothesis testing to check the claim mentioned in introduction part of the paper.
Null hypothesis: There is no significant difference in time spent on sports between the genders
Alternative hypothesis: There is a significant difference in time spent on sports between the genders.
I test this hypothesis using independent samples Student’s t-test.

a=0.05

## Perform testing:

Two-Sample T-Test and CI: Time; Gender
Two-sample T for Time
Gender N Mean StDev SE Mean
0 46 6,76 3,81 0,56
1 37 6,92 3,45 0,57
Difference = mu (0) - mu (1)

## Estimate for difference: -0,158

95% CI for difference: (-1,763; 1,447)
T-Test of difference = 0 (vs not =): T-Value = -0,20 P-Value = 0,845 DF = 81
Both use Pooled StDev = 3,6534
Since p-value of the test is 0.845>0.05, I failed to reject the null hypothesis. I have no evidence to say that there is a significant difference in time spent on sports between the genders (at 5% level of significance).

## Conclusion

The analysis shows that there is no difference in time spent on sports between women and men. Both genders are spend approximately equal time on gym per week. However, there is a number of factors which could bias my results.
The first factor is that the answers of sportsmen were subjective. Each individual reported his or her own opinion about how many hours is being spent on gym. But this estimation is not accurate. Some people feel time better, some feel it worse. Somebody like to lie to make an impression of a great sportsman. It would be better if I could check their indications by my own – if I’d be able to spend a week in a gym observing each sportsman, for how many hours he or she visited the gym.
The second factor is that the men’s data is not seems to be normally distributed. It may affect the result of t-test, because the normality of distribution is the basic assumption of the test. This issue may be resolved if I increase my sample (remember Central Limit Theorem).
The third factor is that I observe the data only during one day. May be the other days of the week (or even of the year) are characterized with another content of sportsmen and the data may report a significantly different result.
The fourth factor is that I have observed only 1 gym. This gym may have preferences for one gender, which bias the number of visitors by gender. It may have more exercise machines for males (for example) and less for females or vice versa. It also could affect the visitors and their attitude to the time spent on gym. This issue could be resolved if I perform my study in different gyms.

## References

Boneau, C. Alan. "The Effects of Violations of Assumptions Underlying the T Test."Psychological Bulletin: 49-64.

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