Statistics 3 x

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Apr 3, 2024

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Statistics Exercise III Caryn Patel California Southern University Activity 7: Statistics Exercise III Dr. Jamie Mills PHD March 28,2024

2 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 . (two -independent-sample t-test)  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. (one-sample t-test; oneindependent sample t-test)  A researcher matches right-handed and left-handed siblings to test whether righthanded siblings express greater emotional intelligence than left-handed siblings. (related samples t-test using the matched-pairs design).  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. (related samples t-test using the repeated measures). #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. This indicates that there's a 95% confidence that the true population mean, encompassing 25

3 professional basketball players between 6 feet, 1 inch and 6 feet, 9 inches, falls within this range. Conversely, there's a 5% probability that the population mean lies outside of this interval.  If the sample were smaller, would the confidence interval become smaller or larger? Explain. As the sample size decreases, the confidence interval expands, accommodating greater variability within the sample.  If you wanted a higher level of confidence (99%) would the confidence interval become smaller or larger? Explain. Increasing the confidence level to 99% would result in a wider confidence interval. This is because the confidence level (LoC) and the confidence interval (CI) have a direct and linear relationship. Raising the LoC expands the CI. When confidence level increases, so does the standard of error, leading to a broader confidence interval.  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? 1. The partner is from .60 to 1.76 years older than the participant 2. The participant is from .60 to 1.76 years older than the partner 3. The partner is from 5.88 to 9.45 years older than the participant

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