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In this study we the factors affecting amount of exercise are determined. The findings of the study are based on sample data collected from 151 anonymous respondents consisting of college students. The respondents are comprised of a diversity of students based on gender, nationalities, ethnicity, etc.

Sample

In this section, the sample characteristics are discussed. They comprise of the categorical and quantitative characteristics of the sample data collected. The pie chart below shows the composition of the sample by the domicile of the students.

35% of the students sampled were domiciled in the UK, 34% were domiciled in EU while the remaining 31% were international. UK domiciled students have the largest proportion.

The table below shows students’ distribution by gender.

66% of the sampled students are male while 30% is female. 4% of the students did not disclose their gender. Thus, the sample is majorly biased towards male respondents than female respondents.

We need to determine the working status of the students. The chart below shows the composition of the students by those who worked part time and those who did not.

79% of the sampled students worked part-time while 21% of the students did not work.

We need to determine the students’ age. The chart below shows the composition of the students by their age.

The largest proportion of the students are between 18 and 19 years. 61% of the students are between 18 to 19 years old, 9% are between 20 and 21 years while 30% are over 21 years.

Analysis

The aim of the study is to determine the factors affecting the amount of exercise. The table below shows the descriptive statistics for time to university, duration of computer use, and minutes of exercise.

Time To University?

Duration On A Computer?

Minutes Of Exercise?

Mean

38.80795

Mean

89.59603

Mean

141.8675

Standard Error

2.589616

Standard Error

6.209536

Standard Error

11.42791

Median

30

Median

60

Median

120

Mode

30

Mode

120

Mode

120

Standard Deviation

31.82174

Standard Deviation

76.30406

Standard Deviation

140.4286

Sample Variance

1012.623

Sample Variance

5822.309

Sample Variance

19720.18

Kurtosis

-0.10313

Kurtosis

8.759597

Kurtosis

3.445956

Skewness

0.932481

Skewness

2.2742

Skewness

1.655555

Range

132

Range

497

Range

720

Minimum

3

Minimum

3

Minimum

0

Maximum

135

Maximum

500

Maximum

720

Sum

5860

Sum

13529

Sum

21422

Count

151

Count

151

Count

151

The average time taken to commute to university is 38.81 minutes with a standard deviation of 2.59. The minimum time for commute is 3 minutes while the maximum time is 135 minutes. The average time of computer use is 89.60 minutes with a standard deviation of 6.2 minutes. The minimum time of computer use is 3 minutes while the maximum time is 500 minutes. The average time taken to exercise is 141.87 minutes with a standard deviation of 11.43. The minimum time for exercise is 0 while the maximum time is 720 minutes.

A regression analysis with gender, commute, and computer use as the independent variables is conducted. The amount of time taken to exercise is the dependent variable for the study. The table below shows the regression results for the analysis.

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

169.3445

26.28628

6.442317

1.73E-09

117.3784

221.3107

Gender

-24.4474

25.99176

-0.94058

0.348528

-75.8313

26.93656

Commute

-0.25492

0.392917

-0.6488

0.517525

-1.03169

0.521846

Computer

-0.09002

0.157046

-0.57323

0.567399

-0.40049

0.220444

The following regression equation can be used to predict the amount of time taken exercising.

Time taken exercising = 169.3445 – 24.4474(gender) – 0.2549(Commute) – 0.0900(Computer)

The three independent variables are insignificant predictors of the dependent variable because the p-values are greater than the level of significance, 5%.

An analysis of variance is conducted to determine the significance of the regression model. The table below shows the results of the ANOVA analysis.

ANOVA

df

SS

MS

F

Significance F

Regression

3

33294.29

11098.1

0.551197

0.648156

Residual

141

2838968

20134.52

Total

144

2872262

The test statistic is 0.5512 while the p-value is 0.6482. The test statistic is not significant because the p-value is greater than the level of significance, 5%. Therefore, the regression model developed is not a significant predictor of the dependent variable.

Conclusion

The test shows that the independent variables are insignificant. This implies that gender, time taken in commute and time for computer use do not have a significant effect on the amount of exercise for the students. It would be important to investigate other variables that affect the amount of exercise.

Task 2

In this test we shall investigate the relationship between the time taken from the student’s accommodation to Coventry University and the time spent doing moderate or vigorous exercise per week. The time spent doing moderate or vigorous exercise per week is the dependent variable while the time taken from the student’s accommodation to Coventry University is the independent variable. A regression analysis will be conducted to investigate the relationship. First, we need to investigate whether there is a linear relationship between the dependent variable and the independent variable. The scatter plot below shows the relationship between the tw variables.

The scatter plot above shows that there is negative relationship between the time of commute and the amount of exercise. A regression analysis is carried out. The table below shows the results of the regression analysis.

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

149.6305

18.10087

8.26648

7.02E-14

113.8629

185.398

Time To University?

-0.20003

0.361154

-0.55388

0.580495

-0.91368

0.51361

The following regression equation can be obtained.

Amount of exercise = 149.6305 – 0.2 (time of commute)

The intercept of the equation is 149.6305 while the slope is 0.2. The intercept implies that students who live within the university with 0 minutes of commute are expected to have 149.63 minutes of exercise on average. The slope of the equation implies that students’ amount of exercise decreased by 0.2 minutes for every additional minute of commute to the university.

The table below shows the results of correlation analysis for the regression model.

Regression Statistics

Multiple R

0.045329

R Square

0.002055

Adjusted R Square

-0.00464

Standard Error

140.7542

Observations

151

The R square value of the regression model is 0.002055. This implies that 0.21% of the variation in the dependent variable is attributed to changes in the independent variable.

Using the regression model above, we can predict the amount of exercise for the following minutes of commute.

a) 25 minutes

Amount of exercise (in minutes) = 149.6305 – 0.2 (25) = 144.63 minutes.

b) 35 minutes

Amount of exercise (in minutes) = 149.6305 – 0.2 (35) = 142.63 minutes.

Finally, we need to investigate the significance of the independent variable. The table below shows the results for analysis of variance on the significance of the model.

ANOVA

df

SS

MS

F

Significance F

Regression

1

6077.799

6077.799

0.306778

0.580495

Residual

149

2951950

19811.74

Total

150

2958027

The test statistic, F is 0.3068 while the p-value is 0.58. The test statistic is insignificant because the p-value is greater than the level of significance. Therefore, the regression model is not significant. In addition, the t statistic for the significance of the independent variable is not significant. Therefore, the time taken to commute to the university is not a significant variable for the regression model.

Task 3

We need to analyze the key activities required for the redesign of a television. The figure below shows the network diagram for the project.

Using the above network diagram and the information provided, we can develop the following precedence diagram for the project.

Using the above diagram, we can develop the following paths.

Path 1: A-C-E-G-H-I-K-L = 7+3+4+1+7+3+1 = 26

Path 2: A-C-E-G-H-J-K-L = 7+3+4+1+7+2+1 = 25

Path 3: B-D-F-G-H-I-K-L = 3+2+2+1+7+3+1 = 19

Path 4: B-D-F-G-H-J-K-L = 3+2+2+1+7+2+1 = 18

The critical path is A-C-E-G-H-I-K-L.

In addition, we can calculate the float for the activities in path 2, path 3 and path 4. The float for all activities in path 1 is zero because it is the critical path.

Float for path 2 = 26 – 25 = 1

Float for activities

Activity A: float = 0| Activity C: float = 0| Activity E: float = 0| Activity G: float = 0| Activity H: float = 0| Activity J: float = 1| Activity K: float = 0

Float for path 3 = 26 – 19 = 7

Float for activities

Activity B: float = 4| Activity D: float = 1| Activity F: float = 2| Activity G: float = 0| Activity H: float = 0| Activity I: float = 0| Activity K: float = 0

Float for path 4 = 26 – 18 = 8

Activity B: float = 4| Activity D: float = 1| Activity F: float = 2| Activity G: float = 0| Activity H: float = 0| Activity J: float = 1| Activity K: float = 0

The complete duration for the project is determined by the longest path. Thus, the complete duration for the project is the duration of the critical path. This implies that the complete duration is 26 weeks.

September 25, 2023

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