PSYC FPX 3700 Assessment 3

Student Name

Capella University

PSYC-FPX3700 Statistics for Psychology

Prof. Name:

Date

Part 1: Introduction to Hypothesis Testing

Overview of the Dataset

For this analysis, the dataset titled Assessment_3a_Data.csv (available on the Assessment 3 Canvas page) was utilized. This is a hypothetical dataset representing a sample of grocery store customers. Each observation corresponds to a customer and includes the following variables:

Variable Name	Measurement Level	Description
Customer_ID	Nominal	A unique identification number assigned to each customer
Gender	Nominal	Customer’s self-reported gender identity
Age	Ratio	Customer’s self-reported age in years
Purchase_Amount	Ratio	Amount spent during the visit
Prepared_Food	Nominal	Indicates whether the customer purchased prepared food
Shopper_Card	Nominal	Indicates whether the customer used their shopper’s card

Assessment Criteria

The following objectives were addressed:

Formulate hypothesis statements for the given scenario.
Conduct a binomial test in JASP.
Evaluate the statistical significance of the results.
Interpret findings in a clear, non-technical manner for general audiences.

Research Question

The marketing department of the grocery store posed the question:

Are more than half of all grocery store customers women?

This question aims to determine if the proportion of female customers exceeds 50% of the total customer base.

Hypothesis Statements

The hypotheses were formulated as follows:

Hypothesis	Statement
Null Hypothesis (H₀)	The proportion of customers identifying as women equals 0.50 (50%).
Alternative Hypothesis (H₁)	The proportion of customers identifying as women is greater than 0.50.

Mathematically,
H₀: p = 0.50
H₁: p > 0.50

Statistical Analysis

A binomial test was conducted using JASP to examine whether the proportion of female customers was significantly greater than 0.50.

The test results indicated that 61 out of 97 customers (62.9%) identified as women. The results of the binomial test were statistically significant, p = .014. Because p < .05, the null hypothesis was rejected, suggesting a higher proportion of women shoppers than men.

Statistical Output	Result
Sample Size (N)	97
Female Customers	61
Proportion of Females	62.9%
Test Proportion	50%
p-value	.014
Decision	Reject H₀

Interpretation for a Non-Technical Audience

The test examined whether women made up more than half of the grocery store’s customers. Out of 97 customers surveyed, about 63% were women. The statistical analysis showed that this difference was unlikely due to random chance (p = .014). Therefore, it can be concluded that women represent the majority of this grocery store’s customers.

From a practical perspective, this insight is valuable for marketing strategies and promotional planning. Knowing that the store attracts more female customers could inform targeted advertising, product selection, and customer engagement approaches.

Part 2: Comparing Two Means

Overview of the Dataset

This analysis uses the Assessment_3b_Data.csv file (provided on the Assessment 3 Canvas page). The dataset includes information collected from a sample of students recently admitted to a bachelor’s degree program at a large online university.

Variable Name	Measurement Level	Description
Student_ID	Nominal	Unique identifier for each student
Admit_Status	Nominal	Indicates whether the student was admitted as a first-year (FYR) or transfer (TRN) student
Age	Ratio	Student’s self-reported age in years
FirstGen	Nominal	Indicates whether the student is a first-generation college student (Y/N)
Primary_Degree	Nominal	Indicates the student’s primary degree type (BA, BS, or BSN)

Assessment Criteria

The analysis required:

Computing descriptive statistics (sample size, mean, standard deviation).
Creating histograms to visualize data distribution.
Writing appropriate hypotheses.
Conducting a Welch’s t-test.
Interpreting statistical significance and reporting findings in APA style.

Research Scenario

The admissions office at the online university sought to determine whether first-year (FYR) and transfer (TRN) students differ in their mean age.

Descriptive Statistics

The descriptive statistics for the two groups are summarized below:

Group	N	Mean Age (M)	Standard Deviation (SD)
First-Year Students (FYR)	86	27.30	4.15
Transfer Students (TRN)	69	32.29	7.08

The histograms generated in JASP illustrated that the age distributions for both groups were approximately normal, but with differing spreads, justifying the use of a Welch’s t-test, which does not assume equal variances.

Justification for the Welch’s t-test

The Welch’s t-test was deemed appropriate because:

The analysis involves comparing the mean age of two independent groups (FYR and TRN).
The dependent variable (age) is continuous.
Variances and sample sizes between the groups were unequal.
Thus, Welch’s t-test provides a robust and accurate comparison under these conditions.

Hypothesis Statements

Hypothesis	Statement
Null Hypothesis (H₀)	The mean age of first-year students equals the mean age of transfer students (μ₁ = μ₂).
Alternative Hypothesis (H₁)	The mean age of first-year students differs from the mean age of transfer students (μ₁ ≠ μ₂).

Statistical Results

A Welch’s independent-samples t-test was performed to evaluate whether the mean ages of first-year and transfer students differed significantly. The results were as follows:

Statistic	Result
t(104.4)	−5.18
p-value	< .001
Mean Difference (FYR − TRN)	−4.99 years
95% Confidence Interval	[−6.90, −3.08]
Cohen’s d	−0.86 (large effect size)

APA-Style Summary

A Welch’s independent-samples t-test compared the mean ages of first-year (FYR) and transfer (TRN) students. FYR students (n = 86, M = 27.30, SD = 4.15) were significantly younger than TRN students (n = 69, M = 32.29, SD = 7.08). The difference in mean ages was statistically significant, t(104.4) = −5.18, p < .001. The estimated mean difference was −4.99 years, with a 95% confidence interval of [−6.90, −3.08]. The effect size was large (d = −0.86), indicating a substantial difference in age between the two groups.

Interpretation for a Non-Technical Audience

The results suggest that transfer students are generally older than first-year students. This finding is statistically significant, meaning the age difference is unlikely due to random variation. From a practical standpoint, understanding this demographic difference can assist the admissions office in tailoring support services, advising programs, and communication strategies to meet the differing needs of younger and older student populations.

References

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). APA Publishing.

Gravetter, F. J., & Wallnau, L. B. (2021). Statistics for the behavioral sciences (11th ed.). Cengage Learning.