PSYC FPX 3700 Assessment 3

PSYC FPX 3700 Assessment 3

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Name

Capella University

PSYC-FPX3700 Statistics for Psychology

Prof. Name

Date

Assessment 3 Part 1: Introduction to Hypothesis Testing

For this assessment, the dataset Assessment_3a_Data.csv is used. The data are assumed to represent a sample of customers from a grocery store, collected for the purpose of exploring demographic and behavioral patterns. This hypothetical dataset contains the following variables:

Research Question

The grocery store’s marketing department wants to know:
“Are more than half of all customers women?”

This question seeks to determine whether the proportion of female customers exceeds 50%, which has implications for targeted marketing strategies and customer engagement programs.

Hypothesis Statements

To address the research question, the following hypotheses are formulated:

Conducting the Binomial Test

A binomial test was conducted in JASP to test whether the proportion of female customers exceeded 50%.
The analysis revealed that 61 out of 97 customers (62.9%) identified as women. The test statistic yielded a p value of .014, indicating statistical significance at the α = .05 level. Therefore, the null hypothesis was rejected, suggesting that the proportion of women shoppers is significantly greater than 50%.

Interpretation for a Non-Statistical Audience

The purpose of this analysis was to find out if women make up more than half of the grocery store’s customers. The results showed that approximately 63% of the customers were women, a figure that is statistically higher than 50%. This difference is unlikely to have occurred by chance. In practical terms, this finding implies that women constitute the majority of the store’s customers, which could be valuable for marketing and business decisions—such as tailoring promotions or stocking products that align with female consumers’ preferences.

Assessment 3 Part 2: Comparing Two Means

For this second part, the dataset Assessment_3b_Data.csv is used. These data are assumed to represent a sample of students recently admitted to a large online university’s bachelor’s degree programs. The variables are described below:

Research Question

The admissions office is interested in answering the following:
“Do first-year students and transfer students differ in terms of their ages?”

This question explores whether the mean age differs between students who enter the program as first-year students and those who transfer from another institution.

Choice of Statistical Test

A Welch’s t-test is the appropriate statistical test for this research question. The Welch’s t-test compares the means of two independent groups on a continuous variable and is preferred when the assumption of equal variances is violated. Since first-year and transfer students may have different age distributions and sample sizes, Welch’s t-test provides a more robust analysis compared to the traditional Student’s t-test.

Hypothesis Statements

Results of the Welch’s t-Test

The Welch’s independent-samples t-test compared the mean ages of the two student groups:

The results showed a statistically significant difference in age between the groups,
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].

Because p < .05, the null hypothesis was rejected, indicating that transfer students are significantly older than first-year students on average.

APA-Style Summary of Results

A Welch’s independent-samples t-test was performed to compare the mean ages of first-year (FYS) and transfer (TRN) students. The results showed that FYS 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 age was statistically significant, t(104.4) = −5.18, p < .001, with a large effect size (d = −0.86). The 95% confidence interval for the mean difference (FYS − TRN) was [−6.90, −3.08]. These findings provide strong evidence that transfer students are generally older than first-year students, which could have implications for student engagement and support services within the university.

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.

Gravetter, F. J., & Wallnau, L. B. (2021). Essentials of statistics for the behavioral sciences (10th ed.). Cengage Learning.

JASP Team. (2024). JASP (Version 0.18.0) [Computer software]. University of Amsterdam. https://jasp-stats.org

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