Assignment 4 Statistics Exercise III Related Sample T Confid

Assignment4statistics Exercise Iii Related Sample T Confidence Inter

Assignment 4 Statistics Exercise III: Related-sample t; confidence intervals These weekly exercises provide the opportunity for you to understand and apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance). #1. For each example, state whether the one-sample, two-independent-sample, or related-samples t test is most appropriate. If it is a related-samples t test, indicate whether the test is a repeated-measures design or a matched-pairs design. A professor tests whether students sitting in the front row score higher on an exam than students sitting in the back row. A graduate student selects a sample of 25 participants to test whether the average time students attend to a task is greater than 30 minutes. A researcher matches right-handed and left-handed siblings to test whether right-handed siblings express greater emotional intelligence than left-handed siblings. A principal at a local school wants to know how much students gain from being in an honors class. He gives students in an honors English class a test prior to the school year and again at the end of the school year to measure how much students learned during the year. #2. A random sample of 25 professional basketball players shows a mean height of 6 feet, 5 inches with a 95% confidence interval of 0.4 inches. Explain what this indicates. If the sample were smaller, would the confidence interval become smaller or larger? Explain. If you wanted a higher level of confidence (99%) would the confidence interval become smaller or larger? Explain. Use SPSS and the data file found in syllabus resources (DATA540.SAV) to answer the following questions. Round your answers to the nearest dollar, percentage point, or whole number. #3. Test to see if there is a significant difference between the age of the participant and the age of the partner. Use a paired-sample t-test and an alpha level of 1%. How would you interpret the results of this test? a. The partners are significantly older than the participants. b. The partners are significantly younger than the participants. c. The age of the participants and partners are not significantly different. d. Sometimes the partners are older, sometimes the participants are older. #4. What is the 95% confidence interval for the difference between participant and partner age? The partner is from .60 to 1.76 years older than the participant The participant is from .60 to 1.76 years older than the partner The partner is from 5.88 to 9.45 years older than the participant The participant is from 5.88 to 9.45 years older than the partner.

Paper For Above instruction

The given set of exercises revolves around fundamental statistical concepts, primarily focusing on t-tests for related samples and confidence intervals, along with the application of statistical software for data analysis. The core intent is to help students understand when to use specific types of t-tests, interpret confidence intervals, and perform hypothesis testing to draw meaningful conclusions from sample data.

First, distinguishing among various t-test types is essential. The scenarios presented suggest different research designs such as independent samples, related samples, and one-sample tests. For example, the comparison between students sitting in front versus back rows involves an independent-samples t-test, as these are separate groups. The examination of whether the time students spend attending to a task exceeds 30 minutes is a one-sample test, where the sample mean is compared against a known value. The matched-siblings emotional intelligence study employs a related-samples t-test in a matched-pairs design, as the same individuals are measured under different conditions. Finally, evaluating students' gains before and after an honors class involves a repeated-measures related-samples t-test, as the same students are tested twice, and changes are analyzed.

Next, interpreting the confidence interval around the mean height of professional basketball players helps understand the precision of the estimate. A 95% confidence interval of 0.4 inches around the mean height implies that, if many such samples are taken, approximately 95% of the computed intervals will contain the true population mean height. A wider sample size reduces the margin of error, thus narrowing the confidence interval, making the estimate more precise. Conversely, increasing the confidence level from 95% to 99% enlarges the interval because a higher confidence requires capturing a broader range that likely includes the true mean, reflecting increased uncertainty.

Applying SPSS for data analysis facilitates hypothesis testing and confidence interval estimation. For instance, conducting a paired-sample t-test between participant and partner ages allows assessing whether their mean ages significantly differ at the 1% significance level. Based on the obtained p-value, the conclusion can be that either there is a significant difference with directionality (either partners are older or younger) or no significant difference. The interpretation hinges on the significance level and p-value.

Furthermore, establishing the confidence interval for the difference in ages informs about the magnitude and direction of the age difference. For example, a 95% confidence interval from 0.60 to 1.76 years indicates that the partner is, on average, between approximately 0.6 and 1.76 years older than the participant, with the interval not including zero, suggesting a significant difference.

In conclusion, understanding the proper application of different t-tests is essential for accurate data analysis, and interpreting confidence intervals provides valuable insight into the precision of sample estimates. Using statistical tools like SPSS enhances the robustness of findings, facilitating sound conclusions that support evidence-based decision-making in research contexts.

References

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