Activity 7- Statistics Exercise III

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Statistics

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Jan 9, 2024

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#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. o Two-independent-sample – The professor is comparing the scores of two independent groups the students in the front row and students in the back. This test will determine if there is a significant difference between the two groups.  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. o One-sample t-test – this test is utilized because we are testing one sample mean.  A researcher matches right-handed and left-handed siblings to test whether right-handed siblings express greater emotional intelligence than left-handed siblings. o Related samples t-test/ matched pairs design because the researcher is interested in comparative outcomes.  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. o Related sample t-test which is utilizing repeated-measure design to decrease the bias in the final decision. #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. o With a confidence interval of 95% and a margin of error of .4 inches. The interval would be 6 feet and 4.6 inches (lower boundary) and 6 feet and 5.4 inches (upper boundary)  If the sample were smaller, would the confidence interval become smaller or larger? Explain. o If the sample size was small the confidence interval would become larger. This is occurring because the sample mean is inversely connected to the CI. A small sample size will also lead to a larger standard of error. With a larger standard of error comes a wider confidence interval. Increasing a sample size will

increase the power and will likely lead to detecting and effect and will lead to rejecting the null hypothesis.  If you wanted a higher level of confidence (99%) would the confidence interval become smaller or larger? Explain. o If you want a higher level of confidence, such as 99%, the confidence interval would become larger and you would have a 1% chance of being wrong and there will be more of a likelihood of an event to occur. #3. a. The partners are significantly older than the participants. First, I want to determine if the t value is larger than the critical value (CV). I have found that based on the t distribution table, the CV is 2.5882, based on 399 degrees of freedom (df) and alpha level of .01. Our t value of 4.004 is significantly larger than the CV value. Second, I want to see if the p-value is less than .01. Our p-value is .000, which is less then .01. Lastly does the 99% confidence interval cross zero. As you can see both the lower (-1.939) and upper (-.416) numbers are negative meaning that they are on the same side of zero and do not cross zero. This concludes that the null hypothesis is outside the confidence interval and the decision is to reject the null hypothesis, which means there is significant difference between participants and age of partners. While my version of SPSS does not provide the check box to calculate effect size, I can manually provide this information by utilizing the formula Cohen’s D which will provide the effect size. I will be utilizing the means from the paired sample statistics and the standard deviation from the paired sample test to calculate the Cohen’s D score. d = M1 -M2 / SD

.2003 = 34.30 – 33.12 / 5.882 d = .20 Because the null hypothesis is outside of the confidence interval, we can use the effect size to estimate the difference between the null hypothesis and the lower confidences limit. The effect size of d = .20 and would be considered medium effect. #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 The confidence interval is the range of possible values of which a population parameter is likely to contain. The lower and upper boundaries are the confidence limits that are given within a specific level of confidence. In our case our confidence level is 95%.

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