Slide 1 of 10: MAT 1260 Project II: Enrollment Status and Hours Worked

MAT 1260 Project II: Enrollment Status and Hours Worked

01Project

MAT 1260 Project II: Enrollment Status and Hours Worked

Part-time: 25%. Average work hours: 23.05.

For my project, I asked 40 college students two questions.

My questions were about enrollment status and hours worked per week.

Sample size: 40
Topics: 2

Analysis path

Analysis path
Step	Label
1	Survey Data
2	Sample Statistics
3	Confidence Intervals
4	Hypothesis Tests
5	Conclusions

Data Collection and Variables

02Data

Data Collection and Variables

My sample was not perfect because it was a convenience sample.

My sample was 40 college students.

Enrollment status is qualitative. Hours worked per week is quantitative.

Are you a full-time or part-time college student?

Sample size: 40

Variable	Type	What I measured
Enrollment status	Qualitative	Full-Time or Part-Time
Hours worked	Quantitative	Hours worked per week

SubjectEnrollmentHours

1Full-Time20

2Full-Time22

3Full-Time15

4Full-Time0

5Full-Time18

6Full-Time28

7Full-Time12

8Full-Time16

Qualitative Analysis: Full-Time vs Part-Time

03Qualitative Analysis

Qualitative Analysis: Full-Time vs Part-Time

25% of my sample was part-time. The given 2022 value was 10.8%.

Qualitative question - Are you a full-time or part-time college student?

I used the Part-Time category because the 2022 comparison value was 10.8%.

n: 40
x: 10
p-hat: 10 / 40 = 0.25
q-hat: 1 - 0.25 = 0.75
2022 comparison value: 10.8%

Enrollment Status of Surveyed Students

Enrollment Status of Surveyed Students
Category	Frequency	Note
Full-Time	30
Part-Time	10

Part-Time Rate: Sample vs 2022

Part-Time Rate: Sample vs 2022
Measure	Value	Marker
Sample	25%
2022 value	10.8%

Confidence Interval for the Part-Time Proportion

04Qualitative Inference

Confidence Interval for the Part-Time Proportion

We are 95% confident that the population proportion is between 11.58% and 38.42%.

I am finding the 95% confidence interval for the proportion of college students who are part-time.

p-hat = 0.25, q-hat = 0.75, n = 40

Set up $\hat{p} = \frac{x}{n} = \frac{10}{40} = 0.25 \hat{q} = 0.75$
Formula $\hat{p} \pm z_{α / 2} \sqrt{\frac{\hat{p} \hat{q}}{n}}$
Substitute $0.25 \pm 1.960 \sqrt{\frac{(0.25) (0.75)}{40}}$
Interval $0.25 \pm 0.1342 = (0.1158, 0.3842)$

95% z Confidence Interval

Hypothesis Test: Has Part-Time Enrollment Increased?

05Qualitative Inference

Hypothesis Test: Has Part-Time Enrollment Increased?

At alpha = 0.05, I tested if the part-time proportion has increased from 10.8%.

H0: p = 0.108

There is enough evidence to support the claim that the part-time proportion has increased.

Hypotheses $H_{0} : p = 0.108 H_{1} : p > 0.108$
Formula $z = \frac{\hat{p} - p_{0}}{\sqrt{\frac{p_{0} (1 - p_{0})}{n}}}$
Substitute $z = \frac{0.25 - 0.108}{\sqrt{\frac{0.108 (1 - 0.108)}{40}}} = 2.8935$
Compare $z_{c} = 1.6449 p-value = 0.0019$

Right-Tailed z Test

Quantitative Analysis: Hours Worked Per Week

06Quantitative Analysis

Quantitative Analysis: Hours Worked Per Week

The sample mean was 23.05 hours, which is lower than 28 hours.

Quantitative question - How many hours per week do you work?

n = 40, x-bar = 23.05, s = 9.5835; mu0 = 28.

n: 40
x-bar: 23.05
s: 9.5835
mu0: 28
Minimum: 0
Maximum: 42

Distribution of Hours Worked Per Week

Distribution of Hours Worked Per Week
Bin	Frequency	Value range
0-9	3	0 to 9
10-19	10	10 to 19
20-29	16	20 to 29
30-39	9	30 to 39
40-49	2	40 to 49

Mean Hours: Sample vs 2017

Mean Hours: Sample vs 2017
Measure	Value	Marker
Sample mean	23.05 hr
2017 mean	28 hr

Confidence Interval for Mean Hours Worked

07Quantitative Inference

Confidence Interval for Mean Hours Worked

We are 90% confident that the mean is between 20.4969 and 25.6031 hours.

I am finding the 90% confidence interval for mean weekly work hours.

Since the population standard deviation is unknown, I used t.

Formula $\bar{x} \pm t_{α / 2, 39} \frac{s}{\sqrt{n}}$
Substitute $23.05 \pm 1.6849 (\frac{9.5835}{\sqrt{40}})$
Margin $23.05 \pm 2.5531$
Interval $(20.4969, 25.6031)$

90% t Confidence Interval

Hypothesis Test: Have Weekly Work Hours Decreased?

08Quantitative Inference

Hypothesis Test: Have Weekly Work Hours Decreased?

At alpha = 0.10, I tested if the mean number of work hours is below 28.

H0: mu = 28

There is enough evidence to support the claim that weekly work hours have decreased.

Hypotheses $H_{0} : μ = 28 H_{1} : μ < 28$
Formula $t = \frac{\bar{x} - μ_{0}}{\frac{s}{\sqrt{n}}}$
Substitute $t = \frac{23.05 - 28}{\frac{9.5835}{\sqrt{40}}} = - 3.2667$
Compare $t_{c} = - 1.3036 p-value = 0.0011$

Left-Tailed t Test

Results Summary

09Results

Results Summary

Both tests rejected H0.

For enrollment status, the sample part-time rate was 25%.

For work hours, the sample mean was 23.05 hours.

Sample part-time rate: 25%
2022 part-time rate: 10.8%
Sample mean hours: 23.05
2017 mean hours: 28

Topic	Given Value	Sample Value	Test Conclusion
Part-time proportion	10.8%	25%	Evidence of increase
Mean work hours	28	23.05	Evidence of decrease

Final Conclusion and Limitations

10Conclusion

Final Conclusion and Limitations

My sample may not represent all college students because it was a convenience sample.

The surprising result was a higher part-time rate but lower average work hours.

I expected students to work more hours, but my sample did not show that.

Sample size: 40
Part-time comparison year: 2022
Work-hours comparison year: 2017

Final answer

Part-time25%

Given 2022 value: 10.8%

Work hours23.05

Given 2017 mean: 28

Sample40

Convenience sample

My sample may not represent all college students.