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This assignment aims at establishing a basic familiarity with fundamental concepts of research methods including research design, data collection, quantitative research, statistical analysis and report writing. On completion of this assignment, you should be able to have basic understanding of:

  • statistical analysis for quantitative research
  • quantitative research

(1)Data collection:

Collect the data from at least 20 observations at different time from the library. For each observation at a time, you obtain a counting result of the number of computers which have been occupied during the particular time. Provide a table in the research report to give the counts and the time the data was collected and give an explanation about how data was collected.

(2) Statistical analysis using One-sample T-test 

  1. Give a hypothesis about the mean usage of computers (the mean number of computers occupied), which reflects your research problem;
  2.  Carry out your T-test with statistical computing software (e.g., R);
  3. Draw a research conclusion, including an analysis about your finding.

Now assume you aim at determining if the average usage of computers in the morning equals to that in the afternnon. Illustrate some key points of your research, including the hypothesis testing method you will adopt, the main steps for the testing and possible conclusions.

Bear in mind that you do not need to truely collect data and write code for this sub-task. Just discuss your strategy and potential conclusions.

Follow the report writing requirements studied during the lecture.

Data Collection

The University of Wollongong is located in Australia, delivering transnational education programs in different parts of the world. It consists of a global network of professions focused on promoting world-class teaching programs and experience (Farrell, 2017, 21). The university is committed to providing a five-star learning experience by offering quality facilities to students. Part of these facilities includes a high-rated library that enables students to access different kinds of learning resources and spaces (Daly, 2015, 170). The University of Wollongong library building is well-designed to suitably accommodate a large number of students and visitors looking for study materials (Schlosser et al., 2018, 15). The library is normally opened between 8 am and 10 pm on weekdays and from 10 am to 8 pm on weekends. To promote the delivery of quality education and learning experience, the University of Wollongong library provides students to access computers and technological resources required for the provision of digital information (Cox and Jantti, 2015, 66). The ground floor of the library provides most of the library services and consists of study space and computer spaces (Showers, 2015, 113). It is estimated that 66 computers are accommodated on the ground floor. In this research, the main interest is to examine the usage of computers on the ground floor of the University of Wollongong Library.

For the study to be effective, the data collection process was performed. Data collection is a process that involves gathering information and measuring the variables of interest necessary for answering the stated research question (Frost, 2019, 23). Besides, variables measured in the data collection process enable the test hypothesis to be evaluated (Bain, 2017, 210). In this research, the quantitative study methodology is used. The data collection involved observation and recording of computers available on the ground floor of the library and the number of computers in use.

The data collection exercise was conducted from October 7, 2019, to October 11, 2019. This process was taking place on weekdays, considering these are the busiest days in the university. The data were collected at four different times resulting in a total of 20 observations made. During this period of data collection, the number of computers occupied were counted and recorded. Data were collected in the morning, lunch, afternoon and evening hours. The table below displays the data collected from October 7, 2019, to October 11, 2019, and the specified time the exercise was conducted.

Data Collection Date

Hours of Data Collection

Time of Observation

Number of Occupied Computers

Monday (October 7, 2019)

Morning

10:00 am

54

Lunch

1:00 pm

27

Afternoon

4:30 pm

30

Evening

8:30 pm

23

Tuesday (October 8, 2019)

Morning

10:00 am

20

Lunch

1:00 pm

48

Afternoon

4:50 pm

30

Evening

9:30 pm

39

Wednesday (October 9, 2019)

Morning

11:00 am

45

Lunch

1:00 pm

40

Afternoon

5:30 pm

26

Evening

7:30 pm

22

Thursday (October 10, 2019)

Morning

9:00 am

31

Lunch

1:30 pm

51

Afternoon

5:30 pm

43

Evening

8:30 pm

30

Friday (October 11, 2019)

Morning

10:20 am

32

Lunch

12:00 pm

55

Afternoon

5:40 pm

23

Evening

9:30 pm

18

Statistical Analysis using One-sample T-test

Table 1: Data for Computers Occupied

A quantitative statistical analysis approach is used to evaluate the data collected on the usage of computers on the ground floor of the University of Wollongong Library. The R software is used to perform statistical tests to evaluate the frequency of computer usages on the ground floor. One-sample t-test is used to test the hypothesis that is formulated in this paper as illustrated below. To conduct the one-sample t-test, it is assumed that the mean number of computers available on the ground floor is equal to 66.

This study aims to determine the total number of computers used at the ground floor of the University of Wollongong Library. This number is investigated at varying times partitioned into four periods between 8 am and 10 pm per day. It is hypothesized that an average of 66 computers is available on the ground floor of the UOW library. The hypothesis used for the one-test statistical test is indicated below.

Hypothesis: All the 66 computers on the ground floor of the UOW library are occupied during the morning the opening hours.

The null and alternative hypotheses are formulated as displayed below to help in verifying the validity of the hypothesis above.

Null hypothesis: All 66 computers on the ground floor of the UOW library are occupied.

The null hypothesis, H0: µ = 66

Alternative hypothesis: Not all 66 computers on the ground floor of the UOW library are occupied.

An alternative hypothesis, H1: µ ≠ 63

After formulating the null and alternative hypothesis based on the average of 66 computers, the one-test analysis is performed using the R software.

Mean

With a sample of 20 observations, n = 20, the mean for the observations is calculated as illustrated in the R code below.

> computers_Occupied<-c(54,27,30,23,20,48,30,39,45,40,26,22,31,51,43,30,32,55,23,18)

> mean(computers_Occupied)

[1] 34.35

The mean number of computers from the sample of 20 observations is 34.35 computers.

Standard deviation

With a sample of 20 observations, n = 20, the standard deviation for the observations is calculated as illustrated in the R code below.

> computers_Occupied<-c(54,27,30,23,20,48,30,39,45,40,26,22,31,51,43,30,32,55,23,18)

> sd(computers_Occupied)

[1] 11.69469

The standard deviation for the 20 observations is 11.69469.

Maximum and minimum number of computers

The minimum number of computers occupied in the 5 days is calculated and displayed below.

> computers_Occupied<-c(54,27,30,23,20,48,30,39,45,40,26,22,31,51,43,30,32,55,23,18)

> min(computers_Occupied)

[1] 18

Similarly, the maximum number of computers occupied in the 5 days is calculated using the R software and displayed below.

Conclusion

> computers_Occupied<-c(54,27,30,23,20,48,30,39,45,40,26,22,31,51,43,30,32,55,23,18)

> max(computers_Occupied)

[1] 55

Graphical representation of the number of computers occupied

> computers_Occupied<-c(54,27,30,23,20,48,30,39,45,40,26,22,31,51,43,30,32,55,23,18)

> barplot(computers_Occupied, main="Number of Computers Occupied”,col="gray”)

The total number of recordings sampled for hypothesis testing is equal to 20 for the 5 days of data collection. One-sample t-test is performed on the 20 observations recorded for the 5 days to examine the validity of the hypothesis specified in this research study. Importantly, the assumptions made on the data are that the dependent variable is normally distributed and independent of each other (Mertler and Reinhart, 2016, 430). The mean number of computers used in the R t-test is 66 computers. The alternative hypothesis is assumed that the mean number of computers is less than 66. The alpha value for the test is 0.05. Therefore, the t-test is conducted using a 95 percent confidence interval.

An R script of the statistical test is displayed below with the results of the calculation.

> computers_Occupied<-c(54,27,30,23,20,48,30,39,45,40,26,22,31,51,43,30,32,55,23,18)

> t.test(computers_Occupied, alternative="less", mu=66)

One Sample t-test

data:  computers_Occupied

t = -12.103, df = 19, p-value = 1.121e-10

alternative hypothesis: true mean is less than 66

95 percent confidence interval:

    -Inf 38.8717

sample estimates:

mean of x

    34.35

Critical Value of t-distribution

> n=20

> alpha=0.05

> df=(n-1)

> qt(alpha,df)

[1] -1.729133

The descriptive statistics indicate that the maximum number of computers occupied recorded in the 20 observations was 55. On the other hand, the minimum number of occupied computers on the ground floor of the UOW library was 18. The mean number of computers occupied on the ground floor was 34.35 with a standard deviation of 11.69469. From these descriptive statistics, it can be concluded that some of the 66 computers on the ground floor remain unoccupied. Based on the maximum number of computers occupied on the ground floor, 11 computers remain unoccupied in the opening hours of the library.

The one-test results show that the t value is -12.103, at a degree of freedom of 19. The sample estimated mean of 34.35 at a confidence interval of 95% is displayed from the results. With a sample of 20 observations, the critical value of t-distribution is -1.729133. The critical value of -1.729133 is less than the alpha level of 0.05. Accordingly, the p-value of the t-test is approximately 0.000, which is lower than the alpha level of 0.05. Therefore, the null hypothesis is rejected using the p-value and critical value results (Crowder, 2017, 347). This suggests that the mean number of computers occupied on the ground floor is lower than the hypothesized mean of 66 computers.

From the results above, the null hypothesis is rejected. Therefore, it is concluded that the 66 computers on the ground floor of the UOW library are not fully occupied in the opening hours. The results imply that the usage of computers on the ground floor is not to the maximum. In the morning hours, a person is likely to find a vacant computer on the ground floor. Also, the findings of the research depict that the ground floor is filled with enough computers that can serve all the library visitors.

The research study uses a one-sample t-test to examine the validity of the hypothesis that all the computers on the ground floor are occupied in the morning hours. Thus, it cannot establish the usage of computers in the afternoon in comparison to the number of computers occupied in the morning. To determine if the average usage of computers in the morning is the same as that in the afternoon, a two-sample t-test analysis will be used (Schabenberger and Gotway, 2017, 241). Also, an analysis of variance (ANOVA) test can be used to compare the means between morning and afternoon computer usage. To conduct the test in the future, the recorded number of computers occupied in the morning should be independent of that in the afternoon (Chambers, 2017, 111). The t-test value will be concluded depending on whether the mean in the morning is greater or less than that in the afternoon (Mead, 2017, 357).

References

Bain, L., 2017. Statistical analysis of reliability and life-testing models: theory and methods. Routledge.

Chambers, J.M., 2017. Graphical methods for data analysis: 0. Chapman and Hall/CRC.

Cox, B. and Jantti, M., 2015. The Library Cube: Revealing the impact of library use on student performance (University of Wollongong). Library Analytics and Metrics: Using data to drive decisions and services, p.66.

Crowder, M.J., 2017. Statistical analysis of reliability data. Routledge.

Daly, R., 2015. Developing responsive Resource Sharing services at an Australian regional university: University of Wollongong Library. Interlending & Document Supply, 43(4), pp.169-173.

Farrell, A., 2017. Archiving the aboriginal rainbow: Building an aboriginal LGBTIQ portal. Australasian Journal of Information Systems, 21.

Frost, C.M., 2019. Quantitative Methodologies in Human Resource Management. SAGE Publications Ltd.

Mead, R., 2017. Statistical methods in agriculture and experimental biology. Chapman and Hall/CRC.

Mertler, C.A., and Reinhart, R.V., 2016. Advanced and multivariate statistical methods: Practical application and interpretation. Routledge.

Schabenberger, O. and Gotway, C.A., 2017. Statistical methods for spatial data analysis. Chapman and Hall/CRC.

Schlosser, M., Hoff, A., Kirschner, J., Swatscheno, J., Browder, R., and Bielavitz, T., 2018. Library Publishing Directory 2019.

Showers, B. ed., 2015. Library Analytics and Metrics: Using data to drive decisions and services. Facet Publishing.

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