Progress Check Use this activity to assess whether you and your peers can: Under appropriate conditions, conduct a hypothesis test about a difference between two population means. State a conclusion in context. Directions Use the drop-down menu to learn about the three steps needed to complete this assignment. Three steps to complete the assignment Context Do undergraduates sleep less than graduate students? A student conducted a study of sleep habits at a large state university. His hypothesis is that undergraduates will party more and sleep less than graduate students. He surveyed random samples of 75 undergraduate students and 50 graduate students. Subjects reported the hours they sleep in a typical night. For this hypothesis test, he defined the population means as follows: � 1 is the mean number of hours undergraduate students sleep in a typical night. \(\mu_2\) is the mean number of hours graduate students sleep in a typical night. Variables Hours: typical number of hours a student sleeps each night Program: undergraduate or graduate Program is the explanatory variable, and the data is categorical. Hours is the response variable, and the data is quantitative. Data Download the sleep2Links to an external site. datafile, and upload the file in StatCrunch. Open the sleep2 data set in the Stats at Cuyamaca College group on StatCrunch (directions – opens in a new tab). Prompt State the null and alternative hypotheses. Include a clear description of the populations and the variable. Explain why we can safely use the two-sample T-test in this case. Use StatCrunch to carry out the test. (directions) My account on Statcrunch is: User Aobeeda2003 Password Abdullah_2008 Copy the content in the StatCrunch output window (text and the table) and paste it into the textbox with your response. State a conclusion in the context of this problem. List of StatCrunch Directions Click here for StatCrunch Directions Module 23 Discussion Board Use the Module 23 discussion board (opens in a new tab) to ask questions or provide feedback about the problems in any Module 23 activity – including this peer-reviewed assignment. Review Feedback Instructor feedback is only available after an assignment is graded. Use these directions (opens in a new tab) to learn how to review feedback.

[order_button_a]

**Step by step guide on how to do the assignment .**

In recent research, the question of whether undergraduates sleep less than graduate students has become a subject of interest. This peer-reviewed assignment will focus on conducting a hypothesis test to determine if there is a significant difference in the average hours of sleep between these two populations. We will define the null and alternative hypotheses, explain why a two-sample T-test is appropriate for this case, and utilize StatCrunch to perform the test. Finally, we will state a conclusion in the context of this problem.

**Null and Alternative Hypotheses**

In the context of this study, we need to establish clear null and alternative hypotheses to guide our hypothesis test. The null hypothesis ($H_{0}$) states that there is no difference in the average number of hours of sleep between undergraduates and graduate students. In contrast, the alternative hypothesis ($H_{1}$) suggests that undergraduates sleep less, on average, than graduate students. To express this statistically, we can define our hypotheses as follows:

$H_{0}:μ_{1}=μ_{2}$ (There is no difference in the mean hours of sleep between undergraduates and graduate students)

$H_{1}:μ_{1}<μ_{2}$ (Undergraduates sleep less, on average, than graduate students)

In these hypotheses, $μ_{1}$ represents the mean number of hours undergraduate students sleep in a typical night, and $μ_{2}$ represents the mean number of hours graduate students sleep in a typical night.

**Appropriateness of Two-Sample T-Test**

The two-sample T-test is a suitable statistical method for comparing the means of two independent samples, in this case, undergraduates and graduate students. It is important to note that the samples are random, and the data is quantitative, specifically the number of hours a student sleeps each night. Since the explanatory variable is the program type (undergraduate or graduate), which is categorical, and the response variable is hours slept, which is quantitative, a two-sample T-test is appropriate for comparing the means of these two groups. Additionally, the test assumes that the two populations have approximately normal distributions.

StatCrunch, a statistical software, can be used to conduct this hypothesis test. By inputting the data from the provided “sleep2” data file, we can calculate the test statistics and determine whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

[order_button_b]

**StatCrunch Hypothesis Test**

To perform the hypothesis test, we will utilize the provided StatCrunch account credentials (User: Aobeeda2003, Password: Abdullah_2008). After logging in, we will upload the “sleep2” data file and carry out the necessary calculations.

The test results from StatCrunch will provide us with key information, including the test statistic, degrees of freedom, p-value, and confidence interval. These results will allow us to make an informed decision about whether we should reject the null hypothesis.

**Conclusion**

Upon conducting the two-sample T-test using StatCrunch, the test results indicate whether we can safely conclude whether undergraduates sleep less than graduate students at a large state university. The output from StatCrunch will include the test statistic, degrees of freedom, p-value, and confidence interval.

If the p-value is less than a chosen significance level (e.g., 0.05), we will reject the null hypothesis and conclude that there is sufficient evidence to suggest that undergraduates, on average, sleep fewer hours than graduate students. Conversely, if the p-value is greater than the chosen significance level, we will fail to reject the null hypothesis, implying that there is no significant difference in the average number of hours of sleep between these two populations.

In conclusion, this assignment aims to answer the question of whether undergraduates sleep less than graduate students by conducting a hypothesis test. We have defined clear null and alternative hypotheses, explained the appropriateness of using a two-sample T-test, and discussed the use of StatCrunch for performing the test. The conclusion will be based on the results of the hypothesis test, providing valuable insights into the sleep habits of these two groups of students.

[order_button_c]

**FAQs (Frequently Asked Questions)**

**What is the significance of comparing sleep patterns between undergraduates and graduate students in a university setting?**

This comparison is significant because it can provide insights into the potential impact of academic workload and lifestyle choices on students’ sleep habits. Understanding these patterns can help universities tailor support services and interventions for students.

**How were the random samples of 75 undergraduate students and 50 graduate students selected for this study?**

The details of the sampling method used in this study are not provided in the initial question. It is essential to ensure that the samples are truly random and representative of the larger undergraduate and graduate student populations.

**What statistical software can be used besides StatCrunch for conducting the two-sample T-test in this study?**

While StatCrunch is a popular tool, other statistical software like R, SPSS, or Excel can also be used to perform a two-sample T-test. The choice of software may depend on the researcher’s familiarity and access to these tools.

**Why is a two-sample T-test suitable for comparing the sleep patterns of undergraduates and graduate students in this context?**

A two-sample T-test is appropriate as it is designed for comparing means between two independent groups. It assesses whether there is a significant difference in sleep hours between these two populations, making it a relevant choice for this study.

**What would the results of the hypothesis test reveal if the null hypothesis is rejected in this study?**

If the null hypothesis is rejected, it would suggest that there is enough statistical evidence to conclude that undergraduates sleep fewer hours, on average, compared to graduate students. This could have implications for student support and well-being programs.