PSYC FPX 3700 Assessment 3

Student Name

Capella University

PSYC-FPX3700 Statistics for Psychology

Prof. Name

Date

Assessment 3 Part 1: Introduction to Hypothesis Testing

This assessment involves working with the Assessment_3a_Data.csv dataset, available on the Assessment 3 page in Canvas. The dataset represents hypothetical information gathered from a random sample of grocery store customers. The purpose of this assessment is to explore hypothesis testing using real-world data scenarios.

Dataset Description

The dataset includes the following variables:

Variable	Type	Description
Customer_ID	Nominal	A unique identifier assigned to each customer
Gender	Nominal	Customer’s self-reported gender identity
Age	Scale	Customer’s self-reported age in years
Purchase_Amount	Scale	Total amount spent during the visit
Prepared_Food	Nominal	Indicates if the customer purchased any prepared food (Yes/No)
Shopper_Card	Nominal	Indicates if the customer scanned their shopper’s card (Yes/No)

The task is to determine whether more than half of the customers identify as women using a binomial test in JASP.

Research Question

The marketing team at the grocery store wants to know:

“Are more than half of all the store’s customers women?”

This question focuses on testing whether the proportion of female customers exceeds 50%.

Hypothesis Statements

Type	Statement (in Words)	Statistical Notation
Null Hypothesis (H₀)	The proportion of female customers is equal to 50%.	H₀: p = 0.50
Alternative Hypothesis (H₁)	The proportion of female customers is greater than 50%.	H₁: p > 0.50

Conducting the Binomial Test in JASP

A binomial test was performed to determine if the proportion of women shoppers significantly exceeded 50%. The analysis showed that 61 out of 97 customers (62.9%) identified as women. The test results indicated a significant difference, p = .014, which is less than the .05 alpha level. Therefore, the null hypothesis was rejected.

This statistical evidence suggests that more than half of the grocery store’s customers are women.

Decision Regarding the Null Hypothesis

Based on the p-value:

Decision: Reject H₀
Reason: The p-value (.014) is below the significance threshold of .05, indicating a statistically significant result.

Interpretation for a General Audience

The analysis examined whether women make up more than half of the grocery store’s customers. The findings revealed that approximately 63% of the sample were women, which is significantly higher than the expected 50%. This difference is unlikely to have occurred by chance. In practical terms, the grocery store can use this insight to design marketing strategies targeting female customers, such as promoting products and loyalty programs that align with their purchasing preferences. The result is both statistically and practically significant, providing meaningful business insights.Assessment 3 Part 2: Comparing Two Means

This section uses the Assessment_3b_Data.csv dataset, which includes data from students recently admitted to a bachelor’s degree program at a large online university. The goal is to determine if there is a difference in mean age between first-year (FYR) and transfer (TRN) students.

Dataset Description

Variable	Type	Description
Student_ID	Nominal	A unique ID assigned to each student
Admit_Status	Nominal	Indicates whether the student was admitted as a first-year (FYR) or transfer (TRN) student
Age	Scale	Student’s self-reported age in years
FirstGen	Nominal	Indicates if the student is a first-generation college student (Y/N)
Primary_Degree	Nominal	Specifies the degree type (BA, BS, or BSN)

Research Question

“Do first-year students and transfer students differ in their mean ages?”

The purpose of this analysis is to evaluate whether there is a statistically significant age difference between these two independent groups.

Rationale for Using Welch’s t-Test

A Welch’s t-test was selected for this analysis because it compares the means of two independent groups when the assumption of equal variances may not hold. It is more robust than the traditional Student’s t-test, particularly when sample sizes or variances between groups differ. In this dataset, both the group sizes and variability in ages vary between first-year and transfer students, justifying the use of Welch’s test.

Hypothesis Statements

Type	Statement (in Words)	Statistical Notation
Null Hypothesis (H₀)	The mean ages of first-year and transfer students are equal.	H₀: μ_FYR = μ_TRN
Alternative Hypothesis (H₁)	The mean ages of first-year and transfer students are different.	H₁: μ_FYR ≠ μ_TRN

Results of Welch’s t-Test

The Welch’s t-test compared the mean ages of first-year and transfer students:

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

The analysis revealed a significant difference in mean age,
Welch’s t(104.4) = −5.18, p < .001, with a large effect size (Cohen’s d = −0.86) and a 95% confidence interval for the mean difference of [−6.90, −3.08].

Interpretation of Findings

The test results show that transfer students are significantly older than first-year students. The large effect size (Cohen’s d = −0.86) indicates a substantial difference between the two groups, beyond what could be attributed to random variation. This difference may reflect life-stage differences, such as prior college experience or career transitions. The results are both statistically significant and educationally relevant, providing useful insights for admissions policies and student support planning.

Summary in APA Style

A Welch’s independent-samples t-test was conducted to compare the mean ages of first-year and transfer students. The findings showed that first-year students (n = 86, M = 27.30, SD = 4.15) were significantly younger than transfer students (n = 69, M = 32.29, SD = 7.08). The difference in mean age was statistically significant, t(104.4) = −5.18, p < .001, with a large effect size (d = −0.86) and a 95% confidence interval for the mean difference of [−6.90, −3.08]. These results suggest that transfer students tend to be older than first-year students in this university’s bachelor’s programs.

References

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

Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th ed.). Sage Publications.

PSYC FPX 3700 Assessment 3

Gravetter, F. J., & Wallnau, L. B. (2020). Statistics for the behavioral sciences (11th ed.). Cengage Learning.

JASP Team. (2024). JASP (Version 0.18) [Computer software]. https://jasp-stats.org