EXST 2201 Exercises and Study Guide

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EXST 2201 Exercises and Study Guide Rules: Do not remove other's work unless the answer is wrong. Add anything you want that is helpful to the class material. Due to the academic integrity policy, do not put quiz answers or test material in here. ONLY exercises and study material Lesson 4.1 1. In the process of inference, please select the most appropriate answer to the questions below: Lesson 5.1 1. In the process of inference, please select the most appropriate answer to the questions below: a. What is a confidence interval?: An interval estimate of the population mean. b. What is a sample average?: A point estimate of the population mean. 2. Please select how often the statistics below capture the value of the population mean. a. A sample average: Almost never b. A confidence interval: The confidence level number of times 3. What value is in the middle of a confidence interval? a. The value of the sample average. 4. What information does the confidence level give? a. The proportion of times the confidence interval captures the population mean 5. Why does the field of statistics need the method of confidence intervals? a. Because we have uncertain data and the population mean cannot be known. 6. What prior knowledge is the logic of a confidence interval based on? a. The sampling distribution of the sample average 7. Is the interval below a proper denotation of a confidence interval? (101,99) a. 8. In a schematic curve, what area is a confidence interval? a. A middle body area 9. Please match each summary number with what information can add. a. A population mean ( m ): A range of likely values for the sample average. ( m): b. A sample average (x̄): A range of likely values for the population mean 10. The confidence limits in a confidence interval are just the x-values of a middle body area in the schematic curve. a. True 11. For a confidence interval, please match each characteristic with its meaning. a. Its strength: Gives a range of likely, and unlikely, values for the population mean b. Its weakness: Each value inside the interval is equally likely to be the population mean 12. What is the correct equation for a confidence interval? 13. Please match each number in the image below with its part of a confidence interval

a. Half the significance region: Area 1 and Area 3 b. The confidence region: Area 2 c. The critical values: Line 4 14. What is the correct symbol for the size of the significance region? a. Alpha 15. What is the correct equation for the size of the significance region How to find t-values for confidence intervals https://www.dummies.com/article/academics-the-arts/math/statistics/how-to-find-t-values- for-confidence-intervals-169841/ Lesson 5.3 1.) What value is subtracted from the number of data values ( n ) to get the degrees of freedom for a t -distribution? Answer : 1 2.) What is the appropriate situation to use a t -distribution? Answer : When know s , but don't know σ Why : t-Values are appropriate any time you are NOT given the population standard deviation (σ) in the problem, and instead you must use the sample standard deviation (s) 3.) A confidence interval is used to infer the sample average. Answer : False 4.) What values are inside a properly made confidence interval? Answer : Likely values for the population mean. 5.) What is the value of the sample average in the confidence interval below? (96,118) Answer : 107 How to solve : ( 96 + 118 ) 2 6.) What is the value of the margin of error in the confidence interval below? (96,118) Answer : 11 How to solve : ( 118 − 96 ) 2 7.) A local college instructor gave a statistics exam to his class of 31 students where the exam scores were normally distributed with an average score of 80 and a standard deviation score of 10. A competing college knew all their students scored 85 on this test. What is the 95%

confidence interval to help find out how these local college students did in comparison to the competing college students? How to solve: 13.) The population mean must be known to calculate a confidence interval Answer : False Lesson 6.1 1.) Click the two reasons that the method of hypothesis testing is needed. Answer : (50%) To find out how reasonable a chosen value is the population mean. (50%) To find out if the population mean is less than, or greater than, a chosen value.

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2.) In hypothesis testing, what does reasonableness mean? Answer : How close a chosen value is to the population mean. 4.) Please match the following inequalities, and equality, to their meaning in a distribution. Answer: A one-tail to the left situation. Less than Rationale: A one-tail situation in the middle. A one-tail to the right situation. Greater than Rationale: A three-tail situation. A two-tail situation. Not equal to 5.) Click the two assumptions needed for the method of hypothesis testing. Answer : (50%) The individuals were randomly selected. (50%) The sample average is normally distributed. 6.) In hypothesis testing, where does the hypothesized value NOT come from? Answer : From the results of the sample. 7.) In hypothesis testing, how is the close and the far determined? Answer : By converting the situation from the sample distribution into the z , or t , distribution 9.) Why is the method of hypothesis testing calling an inferential method of statistics? Answer : Because it gives the best guess (infers) from the sample for the value of the population mean. Lesson 6.3 When to use - A hypothesis test is appropriate when you want to test if a chosen value for the population mean is a reasonable choice or not

- t -Values are appropriate any time you are not given the population standard deviation (σ), so you must use the sample standard deviation (s) . The degrees of freedom when using the t -distribution will be n−1 - This type of hypothesis test is called a t -Test of the Mean The difference - The t -Table will be used to get critical values and p -values, instead of the z -Table. - The t -Equation will be used to calculate the test statistic, instead of the z -Equation Four steps of the hypothesis testing Step A : Abstract: - Get descriptive statistics and a set of hypotheses. Step 1 : Theorize: - Draw Schematic Curve and get Critical t -Value. Step 2 : Analyze: - Use one of the three approaches to analyze. 16. Critical Value Approach - Compare test statistic with critical value. 17. p-Value Approach - Compare p -Value with alpha (α). 18. Confidence Interval Approach - Compare μ with confidence interval. Step 3 : Conclude - DO Reject, or DO NOT Reject, the Null Hypothesis. 6.3 Exercise 1.) What is the magnitude (ignore mathematical sign) of the critical value for a two-tailed hypothesis test, with: - α =0.01 - n =20 - s =1.35 Answer: Critical value = 2.861

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EXST 2201 Exercises and Study Guide

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