ST3004 Assignment Hypothesis Testing

ST3004 Assignment Hypothesis Testing

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Walden University

ST3004

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Hypothesis Testing

Hypothesis testing is a crucial statistical process that is used to determine the results regarding population characteristics using the data that is gathered in the form of a sample. Researchers define two competing factors by use of the null hypothesis (H 0 ) that there is no effect that exists in comparison to the alternative hypothesis (H 1 ) that major effects do exist. The decision to determine one or another effect by chance or population is carried out using the analysis of the sample based on hypothesis testing (Yu et al., 2022). The research analysis examines the testing of hypotheses using various statistical procedures to evaluate data successfully and draw concrete conclusions.

Part 1- Hypothesis Testing in Research

Hypothesis testing is a critical statistical method that can enable researchers to establish the validity of scientific hypotheses. This begins by making a claim over the population statistics and then testing sample data to either accept or reject this proposal. The data used in Part 1 of this assessment is provided by Whitley and Fuller-Thomson (2017) to examine the area of hypothesis testing by focusing on health characteristics regarding the status of parenting. The aim of this section is to illustrate the analysis of statistical significance between these relationships in terms of chi-square tests to provide a clearer image of the implications of the data (Whitley and Fuller-Thomson, 2017).

Statistically Non-Significant Relationship

In this section, we will present the gender characteristics obtained in Table 1 that show no statistical correlation with parenting status between grandparents and parents (grandparent vs. parent) [See Appendices].

1. Null and Alternative Hypotheses

• Null Hypothesis (H₀): No statistically significant difference in gender and parenting status (grandparent vs. parent) is found.
• Alternative Hypothesis (H₁): Gender and parenting status (grandparent vs. parent) have a statistically significant connection.

2. Explanation of Statistical Significance

Here, Table 1 shows that the chi-square test has a p-value of 0.11 with respect to the characteristic of Gender, and this value is greater than the alpha level, which has been set at 0.05. The p-value is higher than the alpha level we have set, and as such, we have no basis to reject the null hypothesis. The study reveals that gender has no effect on whether a person is a child raiser or a caregiver to the grandparents. So, the statistical data indicate that the relation between gender and parenting status is not meaningful [See Appendices].

3. Conclusion Statement

The p-value of 0.11 exceeds the set alpha level of 0.05, hence leading to the rejection of the null hypothesis. The fact is that it is evidenced that gender has no statistically significant relationship with the parenting roles (that somebody is a parent or a grandparent) [See Appendices].

4. Type II Error Explanation

The given situation would be a Type II error since we reject the hypothesis of the existence of a significant relationship when gender and parenthood status are proving that such a relationship exists (Yang et al., 2023). Findings of the research would indicate that gender has no effect on becoming a grandparent or parent in cases where such differences are present.

Statistically Significant Relationship

The statistical significance of the factor in Table 2, namely, Arthritis, indicates the statistical significance of this variable with parenting status. [See Appendices].

1. Null and Alternative Hypotheses

• Null Hypothesis (H₀): Arthritis and parenting status (grandparent vs. parent) are not statistically related to each other.
• Alternative Hypothesis (H₁): Arthritis and parenting status (grandparent vs. parent) have a statistically significant relationship.

2. Explanation of Statistical Significance

The p-value of the measurement in the Arthritis, which is 0.001, is greater than the alpha value of 0.05. The association between parenting status (grandparent vs. parent) and arthritis is also found to be statistically significant, as the value of p is less than the alpha level (0.05). The prevalence rates show that solo grandparents suffer from arthritis 50.3%, as compared to the prevalence rates of single parents, which do not exceed 17.5% [See Appendices].

3. Conclusion Statement

The p-value of 0.001 is less than the alpha cutoff of 0.05; we reject the null hypothesis. The analysis indicates that there is a statistically significant relationship between the prevalence of arthritis and parenting status since solo grandparents have arthritis more than single parents.

4. Type I Error Explanation

Type I error caused by false positive results would come as a consequence of rejecting a null hypothesis in the context of no actual association between the occurrence of arthritis and parenting factors. This would imply that it is conclusive that arthritis is connected to parenting status when, in the real sense, that is not the case (Kelter, 2022).

Part 2- Performing A Hypothesis Test

Comparing BMI By Smoking Status

1 Hypothesis Test Selection

The difference in the mean score on BMI between smokers and non-smokers should be analyzed with the help of a two-sample t-test (Quiroz-Reyes et al., 2025). This statistical method is necessary in the two-independent groups test (smokers vs nonsmokers) due to the unknown population standard deviation and the possibility of variation in sample standard deviations.

2 One-Tailed Test Justification

The study will need a one-tailed test as we are trying to establish the truth that smokers are characterized by higher values of BMI than nonsmokers (Quiroz-Reyes et al., 2025). The directional hypothesis is present since our research examines the comparison of the BMI levels in smokers who might be heavier than the nonsmokers.

3 Hypothesis Setup

• Null Hypothesis (H₀): The mean BMI of the smokers is the same or lower than that of the nonsmokers.
• Alternative Hypothesis (H₁): The mean body mass index is higher among smokers than non-smokers.

	Smokers BMI	Non-smokers BMI
Mean	28.29821429	30.64067797
Variance	32.72454221	71.28693746
Observations	56	59
Hypothesized Mean Difference	0
df	102
t Stat	-1.749559621
P(T<=t) one-tail	0.041600982
t Critical one-tailed	1.659929976
P(T<=t) two-tail	0.083201964
t Critical two-tailed	1.983495259

Table 1: T-Test: Two-Sample Assuming Unequal Variances

4. Conclusion Statement

The one-tailed test was used to obtain a p-value of 0.0416, which is less than 0.05. The results substantiate the argument that the value of BMI of smokers is likely to be higher than that of nonsmokers, since the null hypothesis was not proven wrong. The outcome is also supported by the t-statistic value of -1.7496, which is lower than the critical value of 1.6599.

5. Findings in the Context of the Research Question: “Do smokers have a BMI that is greater than that of nonsmokers?”

The t-test data obtained confirm the hypothesis that recommends the existence of a difference in the values of BMI between smokers and nonsmokers. The p-value (0.0416), which is below the significance level (0.05), allows one to conclude that smokers have statistically higher mean BMI compared to that of the nonsmokers.

Comparing Weight by Region of The Country

1. Appropriate Hypothesis Test

ANOVA is the most appropriate statistical test that can address this issue. ANOVA testing is most appropriate because the aim is to figure out the differences in the means of weight of North, South, East, and West. The researchers are trying to determine the possibility of statistically significant differences in the average weight in the North, South, East, and West (Burger, 2023).

2. Hypothesis Test in Excel

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
59.7	116	9575.9	82.55086	390.3432
1	116	302	2.603448	1.284858
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	370712.2	1	370712.2	1893.185	5.5002E-113	3.882207
Within Groups	45037.23	230	195.814
Total	415749.4	231

Table 2:Anova: Single Factor

3. Conclusion Statement

ANOVA results indicate a p-value of 5.5002E-113, which is much less than alpha 0.05. The preliminary test provides the opportunity to refute the first hypothesis. The data has provided the conviction that there is a statistically significant difference in the average weights of the North, South, East, and West regions. The value of the F-statistic of 1893.185 is much greater than the critical value of 3.882207, hence the rejection of the null hypothesis is confirmed. The statistical results demonstrate the fact that the average weight has significant differences across the regions (Treskova-Schwarzbach et al., 2021).

4. Findings in the Context of the Research Question

The results of the ANOVA test were derived based on the following research question: “Are the average weights of all four regions equal? The findings suggest there is a substantial difference in the mean weight of at least one of the regions due to the huge F-statistic and huge p-value. The findings have conclusively indicated that the North, South, East, and West regions possess varying average individual weight since their average weight is significantly different.

5. Box Plot of All Four Regions Side by Side

Short Summary for Question 5

The introduced graphical representation shows the patterns of distribution of the weight data by region between the North, South, East, and West regions. Each box plot indicates the distribution of weights by depicting the 5-number summary encompassing minimum values and Q1, median, Q3, and maximum values in order to show the distribution of data and the central location (Treskova-Schwarzbach et al., 2021).

The weight distribution values of the north and the West are similar except at some positions where the two methods have similar medians. The South and East regions are more dispersed in terms of data since the weight data have outliers and wider distributions than the rest of the regions. The box plots visually confirm that the data on weight do not spread equally across all regions, therefore confirming the results of ANOVA tests that indicated that the average weights of regions are different.

Explore Previous Assessment: ST3003 Assignment The Normal Distribution and Confidence Intervals

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