Hypothesis test (Statistics)

2

Statistical Analysis

Synopsis

The research topic: Impact of students working while enrolled in classes

The Research Question: What is the impact of students working while enrolled in the classes?

The research aims at evaluating if the students work too much and as a result spend less time on their class work than they should.

Key variables: Working hours at the job. The key variable will be the number of employment hours worked in a week for part time students.

Finding data: I will randomly sample 30 part time students and ask them how many hours they work at a job in a given week.

Mean calculation

The following numbers were derived from 30 students working as part time.

10, 15, 13, 14, 12, 20, 11, 21, 10, 5, 7, 8, 11, 12, 20, 19, 15, 14, 12, 13, 11, 17, 16, 10, 8, 7, 6, 5, 17, 14

Mean = sum of hours of employment / number of students: 373 / 30

Mean = 12.4333

Median Calculation

This is the middle value of the data set and is gotten by the following evaluation.

Arrangement in ascending order: 5, 5, 6, 7, 7, 8, 8, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 14, 14, 14,15, 15, 16, 17, 17, 19, 20, 20, 21

Median = 12+12 / 2

Impact of Students Working While Enrolled in Classes 1

Median = 12

Standard deviation

To determine, the standard deviation, we must first calculate the variance of the data set and then determine its square root.

X	X-M	(X-M)2
5	-7	49
5	-7	49
6	-6	36
7	-5	25
7	-5	25
8	-4	16
8	-4	16
10	-2	4
10	-2	4
10	-2	4
11	-1	1
11	-1	1
11	-1	1
12	0	0
12	0	0
12	0	0
13	1	1
13	1	1
14	2	4
14	2	4
14	2	4
15	3	9
15	3	9
16	4	16
17	5	25
17	5	25
19	7	49
20	8	64
20	8	64
21	9	81
Sum		587

S = √ (587)/ N-1

S = √ (587)/ 29

S = √20.0471

Standard deviation = 4.4774

Construction of 95% Confidence Interval

The sampling distribution has the mean of 12.4333. Therefore, the standard deviation of:

4.4774 / 5 = 0.8954. One should note that the standard error is the standard deviation of a distribution sample.

Obtaining the limits

Upper Limit: 12.4333 + 1.96 (0.8954) = 14.1882

Lower Limit: 12.4333 - 1.96 (0.8954) = 10.6783

The confidence interval is 10.6783 ≤ (X - µ) ≤ 14. 1882. The figure of 1.96 is based on the 95% area for a normal distribution that has a 1.96 standard deviation from its mean value.

Information needed here!

Hypothesis to verify claim

Ho: µ > 12

H1: µ ≤ 12

From the above calculation, the results show that the mean or the average working hours for the part time students is greater than 12. I have failed to reject the null hypothesis at 95% level of confidence interval. The claim that students spend more time working than on their classwork is true.

Explanation of Results

Depending on the employment status of the students, their capacity to have access to the resources in campus tends to have a negative impact on their level of academic performance. The working college students are faced with few hours to various school support services such as library, labs, and tutoring. Also, these students felt that their allotted time for class work was limited as a result of their working hours. Such factors play a huge role in the retention of students in colleges and the number of years that student spent to complete their degree (Lehmann and Romano, 2010). From the results evaluation, it is evident that students that spend part of their time working, this had a negative impact on the required time spent on classwork.