Mod 8 Course Project
rachrv
rurvina_statisticsprojectproposalmod6_08162016.docxRunning Head: STATISTICS PROJECT PROPOSAL
STATISTICS PROJECT PROPOSAL
Rachel Urvina
Rasmussen College
Difference between the average number of hours per week that men and women exercise
I plan to investigate if there is any difference between the average number of hours per week that men and women exercise. I will survey two groups one group will consist of women while the other will consist of men. This topic will help in improving my skills on carrying out surveys in order to come up with the results. The main aim of my study is to be able to come up with data consisting of two groups both male and female, which I will use in carrying out investigations in order to come up with my conclusion whether there is any difference between the average number of hours per week that men and women exercise.
The data will be collected through a survey which will involve self-administered questionnaire, which contain closed questions and open ended questions where one will be free to answer any question according to his/her knowledge without limitations.
Population represented:
Men aged between 20 to 50 years (approximately 70 in number)
Women aged between 20 to 50 years (approximately 70 in number)
Variables:
Gender: categorical, male or female
Height: quantitative
Weight: quantitative
Age: quantitative
Amount of time spent on exercise each day: quantitative.
I will use random sampling as my sampling strategy since it will reduce the bias in selecting the sample that will represent the whole population.
A copy of the survey will be as follows;
1. What is your gender?
· Male
· female
2. Please indicate your height in figures
……………………………………………………………
3. Please indicate your weight in figures
……………………………………………….........
4. What is your age (please indicate a specific number and not a range)?
…………………………………………………………………………………..
5. What is your average time per day spent on exercise?
……………………………………………………………………..
Statistical methods:
I will use t-Test to examine the Significance of the Difference between the Means of Two Independent Samples that is both the male and female groups.
The hypothesis to be tested is:
Null hypothesis: there is a difference between the average number of hours per week that men and women exercise.
Alternate hypothesis: there is no difference between the average number of hours per week that men and women exercise
The assumptions to be made are:
(i) That the two samples are randomly drawn from normally distributed populations
(ii) That the measures of which the two samples are composed of equal-interval.
From the analysis, I will be able to determine if there is any difference between the average number of hours per week that men and women exercise, and come up with a conclusion for my null hypothesis whether to accept or reject it.
Results
Raw data
|
Weeks |
Men average hours |
Men Average height(ft) |
Men average weight(kg) |
Women average hours |
Women average height(ft) |
Women average weight(kg) |
|
1 |
5.4 |
4 |
63 |
4.7 |
5.0 |
72 |
|
2 |
5.7 |
5 |
71 |
5.6 |
4.2 |
71 |
|
3 |
5.2 |
4.5 |
69 |
4.0 |
4 |
69 |
|
4 |
4.7 |
5 |
73 |
3.6 |
4.1 |
75 |
|
5 |
5.4 |
5 |
75 |
5.6 |
4.0 |
65 |
|
6 |
5.4 |
4 |
66 |
4.7 |
3.9 |
63 |
|
7 |
5.2 |
3.9 |
59 |
4.0 |
3.3 |
68 |
|
8 |
5.2 |
2.5 |
58 |
4.0 |
2.8 |
67 |
|
9 |
6.1 |
2 |
56 |
4.7 |
2 |
61 |
The data displays the average number of hours used by both Men and Women to exercise per week. The survey was carried for nine weeks and a sample size of 70 was used in calculating the hour’s average. Also, the data contain the average weight and height for both Men and Women. The measurements were measured in kilograms and feets respectively.
Frequency distribution table for the variable of interest
|
Men average hours |
Tally |
Frequency |
|
5.4 |
/// |
3 |
|
5.7 |
/ |
1 |
|
5.2 |
/// |
3 |
|
4.7 |
/ |
1 |
|
6.1 |
/ |
1 |
|
Women average hours |
Tally |
Frequency |
|
4.7 |
/// |
3 |
|
5.6 |
// |
2 |
|
4.0 |
/// |
3 |
|
3.6 |
/ |
1 |
Histogram
From the above Men average hours of exercise histogram, Men average hours of 5.4 and 5.2 were quite frequent. However, it is clear that the histogram has the outliers. The outliers are observations that lie outside the overall pattern. In the above histogram, there are two outliers (4.7 and 6.1).The highest number of exercise hours per week in 9 weeks was 6.1 while the least were 4.7.The general shape of the distribution is positively skewed or skewed to the right.
From the above Women average hours of exercise histogram, Women average hours of 4.7 and 4.0 were quite frequent. However, it is clear that the histogram has the outlier. The outlier is observation that lies outside the overall pattern. In the above histogram, there is one outlier (5.6).The highest number of exercise hours per week in 9 weeks was 5.6 while the least were 3.6.The general shape of the distribution is negatively skewed or skewed to the left.
T-test analysis
|
t-Test: Two-Sample Assuming Equal Variances |
||
|
|
|
|
|
|
Men average hours |
Women average hours |
|
Mean |
5.366666667 |
4.544444444 |
|
Variance |
0.1475 |
0.510277778 |
|
Observations |
9 |
9 |
|
Pooled Variance |
0.328888889 |
|
|
Hypothesized Mean Difference |
0 |
|
|
df |
16 |
|
|
t Stat |
3.041381265 |
|
|
P(T<=t) one-tail |
0.003888806 |
|
|
t Critical one-tail |
1.745883676 |
|
|
P(T<=t) two-tail |
0.007777612 |
|
|
t Critical two-tail |
2.119905299 |
|
Interpretation
Since tobs = 3.04 > 2.12 = tcrit (or p-value = 0.008 <0 .05 = α) we reject the null hypothesis; i.e. there is no enough evidence at 5% level of significance to conclude that there is a difference between the average number of hours per week that men and women exercise.
Conclusion
To sum up, the survey conducted by comparing the average number of hours per week that men and women exercise resulted to a different perspective in claim. From the results above, we can conclude that there is no difference between the average number of hours per week that men and women exercise. Therefore, the number of hours both Men and Women exercise are the same.
