CJAD 620 Problem Set 4

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Franklin University *

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620

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Statistics

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Apr 3, 2024

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docx

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Uploaded by JusticeTapirMaster1077

CJAD 620 STATISTICS PROBLEM SET 2 Name: Directions: Complete all the problems below by typing your answers underneath each of the questions. Write the answers using your own words. Please remember to type your name in the space provided above. 1. In your own words, describe the two important principles of the central limit theorem. (5 pts) The central limit theorem is the shape of the sampling size distribution of the mean when drawing repeated samples from a given population. As the sample size increases, the distribution means calculated from the repeated sampling approach are normally distributed. Overall, the shape of the large sampling size distributions is approximately a normal curve (shape) of the given population when graphed. Regardless of the original population, not being normally distributed. 2. What is the difference between the standard deviation and the standard error? (5 pts) Standard deviation describes variability within a single sample, while standard error describes variability across multiple samples of a population. A standard deviation is a measure of variability for a distribution of scores in a single sample or a population of scores. A standard error is the standard deviation in a distribution of means of all possible samples of a given size from a particular population of individual scores. 3. What is the difference between parametric and nonparametric tests? (5 pts) The key difference between parametric and nonparametric tests is parametric tests rely on statistical distributions in data whereas nonparametric do not depend on any distribution. Parametric tests make assumptions about population parameters and also prefer normal data and larger samples. While a nonparametric test does not assume anything about the underlying distribution. Also, offers robustness in the face of skewed data or small sample sizes. 4. Describe in detail the three main assumptions for parametric testing. (10 pts)

The three main assumptions for parametric testing are Normality, Homogeneity of variances, and Independence of the variable. The Normality is data that have a normal distribution or at least symmetric. There is a higher chance of getting a normal distribution with a large sample size. Next Homogeneity of variances is data from multiple groups, that have the same variance. This means that the distribution or spread of scores around the mean is similar in different groups. Lastly, the Independence of the variable is a variable that should have no inherent or natural connection with the outcome measure. 5. What does it mean when a finding is statistically significant? Why might a statistically significant finding not be a practical finding? (10 pts) When a finding is statistically significant the finding can be found as real, reliable, and not due to chance. Statistically significant shows that a sample size is large enough to detect an effect exists in a study but practical finding shows those effects may not be meaningful in a practical context. 6. What is the purpose of a confidence interval? (5 pts) The confidence interval shows the probability that a parameter will fall between a pair of values around the mean. It also shows the degree of uncertainty and certainty in a sampling method. Confidence intervals are constructed using confidence levels of 95% or 99%. The purpose of a confidence interval is to give the range of values for an estimated population parameter rather than a single value or a point estimate. The confidence interval serves as a critical reminder of the estimate limits. 7. How does increasing sample size impact hypothesis testing? (5 pts) Increasing sample size impacts hypothesis testing by making it more sensitive and more likely to reject the null hypothesis when in fact it is false. It also increases the power of the test. 8. Why do we express Cohen’s d in terms of standard deviation rather than standard error? (5 pts) Cohen's d is a measure of effect size, commonly used in statistics to quantify the difference between two groups in terms of their means. It's calculated by taking the difference between the means of the two

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