Statistics Assignment: MATH 1342 Module 7 - Cell Phone Ownership Study

This assignment analyzes survey data from a statistics class to determine if the proportion of students owning cell phones at a large state university is lower than the national average of 80%. The student performs a one-sample Z-test and constructs a confidence interval to compare the sample proportion to the national proportion. The analysis includes identifying variables, exploring the data, and conducting hypothesis testing. The findings indicate that 78% of the students in the sample own cell phones, slightly less than the national average, and the null hypothesis is rejected. The assignment includes tables and a pie chart to represent the data and the calculations of Z-score, p-value, and confidence levels, along with works cited.

Name
Institution
Professor
Date
MATH 1342 (Module 7).
 Reflexive Action
While looking at the idea behind the question, what rings in mind is inferential statistics.
Constructing a confidence interval for the sample proportion fits the question. As depicted by
the excel sheet named ‘DataSet’, intuitively, we cannot hold to the opinion that students in
the university are different from the entire population of students in the United States
(Statcrunch.com).
 Data Analysis.
Data Identification.
In the excel sheet, we find out that variable cell represents a categorical variable of
students with or without a cell phone.
Ho: 80% of the proportion of students possess cell phones.
Ha: the proportion of students possessing cell phones is less than 80%.
Exploration and summary statistics.
The analytics point out that 78% of the students in this sample are in possession of cell
phones (Hopkins). This is depicted in appendix 1. During the coding process, the blanks we
coded DK (Meaning Don’t Know) and were excluded from the analysis. This process yielded
a total sample of 310 students. The remaining 22% of the students had no cell phones. This is
graphically represented by the pie chart in appendix 2.

2
Confidence level and Hypothesis testing.
The test statistics from the one sample Z-test carried out yields a Z-score of -0.71.
Looking at the p-value (0.239), and comparing it with the critical value of 0.05, this is far
much greater than the critical value. Thus, the cause of action is to reject the null hypothesis
(Wenying et al.).
 Summary Findings
It quite appears that the proportion of students in the stat class in possession of cell
phones is 78%. This is slightly less as compared to the national proportion given as 80% of
all college students. For the H0, we conclude that there is no sufficient evidence to prove that
the proportion of college students who own cell phones is less than the national figure.
Works Cited
Deng, Wenying, et al. "Cross-Validated Kernel Ensemble: Robust Hypothesis Test for Nonlinear
Effect with Gaussian Process." arXiv preprint arXiv:1811.11025 (2018).
Hopkins, Will G. "Estimating Sample Size for Magnitude-Based Inferences." Sportscience 21
(2017).

3
Appendix.
1. Table showing proportion.
Frequency Table Count Proportion Percentage
Students with Cell phones 243
0.78387096
8 78%
Students without Cell
phones 67
0.21612903
2 22%
Total 310 1 100%
2. Pie chart representing the data.
243
67
Pie chart Representing the dataset.
Students with Cell phones Students without Cell phones
3. Confidence level and Hypothesis testing.

4
Hypothesis Testing
Procedure
1Stating the
hypothesis
Ho p=
0.
8
Ha p<
0.
8
stating the critical
value
0.05
Finding the z-score
phat 0.783871
(1-phat) 0.216129
Z-Score
-
0.709952
Calculating the P-
value.
p-val =
0.238866
9
Comparing Z-alpha
Zalpha =
1.644853
6
Confidence Level
Sample statistics
number of successes(x)
sample size(n)
Confidence level 0.95
Proportion of
successes(phat) 0.783871
Proportion of failure 0.216129
Critical value 1.6448536
Margin of Error 0.0384526
Confidence Level
Lower 0.7454184
Upper 0.8223235