Revision 2 | Statistics homework help
Checkpoint Overview: The Confidence Intervals & Hypothesis Testing for Quantitative Data Checkpoint is designed to walk you through analyzing quantitative dating using confidence intervals and hypothesis testing.
Before you proceed, we need to look back at the data collected as part of Project 1, to determine how we will further analyze the quantitative data.
1. Which quantitative variable would you like to further investigate?
The variable I would like to further investigate is how much money do people spend on TV subscriptions (yearly).
2. Which categorical variable can we use to split the quantitative variable of interest? (For example, if we had data on teacher salaries, and split it up by experience level, such as novices vs. veterans.)
The categorical variables we can split the quantitative variable is between genders both male and female.
3. Are your two datasets independent or dependent? Explain your answer.
The dataset is independent If you have one dataset with information on TV subscription spending and another dataset with information on gender, and you combine them to analyze how spending varies by gender, these datasets are independent in the sense that one does not depend on the other for its collection.
If the dataset were dependent each individual’s spending data on TV subscriptions is linked directly to their gender in a single dataset, and you are simply examining relationships within that dataset, then they are dependent on each other because the dataset itself is a combination of these variables.
5. Using technology to answer the following:
a. Provide a screen clip of only the Descriptive Statistics for both of your datasets. Be sure to adjust the group names/labels so they describe your data.
6. Use technology, and a 95% confidence level, to answer the following:
a. Provide a screenshot of the entire Stat App readout.
b. What point estimate can we use to construct a confidence interval for the difference between the two datasets? Include appropriate units.
c. What is the margin of error? Include appropriate units.
d. What is the 95% confidence interval? Use interval notation.
e. In 1-2 sentences, interpret the confidence interval in context of the application, using appropriate units.
The 95% confidence interval of [−103, 978] means we are 95% confident that the true difference in yearly TV subscription spending between males and females lies between -103 and 978. This suggests that, on average, males might spend up to 103 less or 978 more on TV subscriptions compared to females.
f. What does the presence or absence of zero in this confidence interval teach us about the research question? Explain, providing context.
The presence of zero in the confidence interval tells me that the data does not provide enough evidence to rule out zero as a possible value.
7. Develop a hypothesis about your population means.
a. Write a sentence describing your developed hypothesis about the two population means.
(Example: I hypothesize that the mean household income in 2020 was higher than the mean household income in 2016.)
I hypothesis that the mean in TV subscriptions for men $721 spending more than the mean for women at $283.
b. Explain what the symbols and OR represent in context.
c. Write the null hypothesis in symbols.
d. Write the alternative hypothesis in symbols.
e. Is your hypothesis test one-tailed or two-tailed?
My hypothesis is one-tailed.
8. Conduct your hypothesis test at a level of significance 5%, .
a. Provide a screenshot of the entire Stat App readout.
![A screenshot of a computer Description automatically generated]()
b. What is your test statistic?
Test statistic= 1.697
c. What is your p-value?
P-value= 0.0531
d. What is your conclusion about the null hypothesis?
I fail to reject the null hypothesis.
e. In 1-2 sentences, write the conclusion of your hypothesis test in context of the application.
Since the p-value 0.0531 is greater than the significance level. We fail to reject the null hypothesis, which means there is insufficient evidence to conclude that the mean amount of time males spend on TV subscriptions is significantly greater than the mean amount of time females spends on TV subscriptions.
Reflection:
9. Personal Reflection: Write a brief paragraph with your personal thoughts on your project and the process. You may wish to include anything which surprised you or things you found to be challenging along the way. What you write here should not be included in your report below.
Reflecting on this project, I found it challenging to deal with the discrepancy in spending between genders, especially with the high values for males skewing the results. It was surprising to see how outliers can influence the mean and the overall distribution. The process of using statistical tools to analyze and interpret the data was insightful and highlighted the importance of considering the shape and spread of data distributions in quantitative analysis.
Report:
10. Write a Final Report for this project. This is a cohesive report, not a series of responses to questions. You will want to use the scaffolded questions above in your project and elaborate where appropriate to summarize the results of your research, in context of your research question.
Use the following guidelines to structure your report:
a. Introduction: Set the stage for your report by providing appropriate background information. (1 paragraph)
This report investigates the differences in yearly spending on TV subscriptions between male and female consumers. The focus is to determine whether there is a statistically significant difference in the average amount spent on TV subscriptions between the two genders. By using descriptive statistics, confidence intervals, and hypothesis testing, this analysis will provide insights into how spending behaviors differ based on gender.
b. Summary Results: (2-3 paragraphs)
i. Summarize the results from your research and discuss the findings of your confidence intervals.
The initial descriptive statistics reveal differences between male and female spending on TV subscriptions. Males have an average yearly expenditure of $721, with a standard deviation of $1,022, indicating high variability and the influence of extreme values. In comparison, females have an average spending of $283 and a standard deviation of $430, suggesting a more stable and less variable spending pattern. The boxplots and histograms for these datasets highlight that males spending is highly skewed to the right, with several extremely high values, while females’ spending distribution is relatively symmetric and concentrated around the lower values.
The confidence interval analysis provides further context. A 95% confidence interval for the difference in mean spending between males and females ranges from -$103 to $978. This interval includes zero, which indicates that we cannot rule out the possibility that there is no difference in mean spending between the two genders. The hypothesis test, conducted at a 5% significance level, involved testing whether males spend more on TV subscriptions than females. The test statistic was 1.697 with a p-value of 0.0531, which is greater than the significance level. Therefore, we fail to reject the null hypothesis that there is no significant difference in spending between males and females.
ii. Discuss the procedure, results, and conclusion of your hypothesis test.
c. Conclusion: Provide an overview of the research you conducted and refer to the information you have learned from completing Project 1 and Project 2 previously. Consider including any conclusions have drawn the entire semester, regarding your original topic of interest, statistical questions, and research questions you have had along the way. Include at least one good statistical question related to your research you would like to investigate further. Include reflections about the project that would add insight. (2 paragraphs)
The research sheds light on the spending patterns of TV subscriptions between genders. The large mean spending for males, combined with high variability, contrasts sharply with the more consistent but lower mean spending observed for females. Although the confidence interval suggests that the true difference in mean spending could include zero, and the hypothesis test indicates that the difference is not statistically significant, these findings highlight the importance of data variability and sample size in statistical analysis.
The semester’s research concluded that the preference for football over basketball among U.S. adults, based on the sample data, is statistically significant and remarkably higher than the previously assumed population proportion. The confidence intervals and hypothesis testing validated the finding, demonstrating the practical application of statistical theories like the Central Limit Theorem in real-world data analysis
Reflecting on the entire process, I learned the importance of ensuring that sample data is representative and meets the assumptions required for statistical inference. The practical challenges included ensuring a representative sample and accurately interpreting the statistical results. This project emphasized how statistical methods can provide insights into population preferences and trends, but also highlighted the need for careful consideration of sample size and sampling methods to ensure valid conclusions
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