# STATS LAST UNIT

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Testing the Difference Between Means (Large Independent Samples) Determining Hypothesis - When samples are independent, we are generally trying to show there is no difference between the samples: H o : μ1 - μ2 = 0 H a : μ1 - μ2 ≠ 0 Conditions that must be met in order to perform the test: - Samples are randomly selected - Independent of each other - At Least 30 Two Sample Z-Test for Difference Between Means Formula: Conducting the Test: 1. State H o and H a 2. Identify a 3. Find Critical Z Value 4. Calculate the test score 5. Compare values and make determination (reject or fail to reject) 6. Interpret the decision IN CALCULATOR: Stat -> Test -> #3 (2-SampZTest) Testing the Difference between Means (Small Independent Samples): Conditions that must be met in order to perform the test: - Samples are randomly selected - Samples are independent of each other - Each population is normally distributed Two Sample t-test for difference between means
If the variances of the populations are equal: - Data is combined to calculate a pooled standard deviation - In calculator (pooled > yes or no) If the variances are not equal: - Degree of freedom is the smaller of n1 - 1 and n2 - 1 Two sample tests for Independence: - Choose between z-test and t-test - If t-test, make sure both populations are normally distributed - If you know both population standard deviations, use z-test - If not, make sure variances are equal Conducting a 2-sample t-test for small independent samples: 1. State null and alternative 2. Identify alpha 3. Calculate degree of freedom 4. Find critical t value 5. Calculate the test score 6. Compare values and make determinations 7. Write conclusion Testing the Difference between Means (Dependent Sample): Conditions that must be met: - Samples are randomly selected - Samples are dependent (paired) - The population normally distributed Find difference in each paired values: - d=x1-x2
Calculate the mean value of the differences: - dbar=(sum of differences)/n Conducting a 2-sample t-test for dependent samples: - State null and alternative - Identify alpha - Calculate degree of freedom - Find critical value - Calculate dbar and s d - Calculate test score - Compare values and make determination - Interpre t decision 9.1 Correlation - The relationship between two variables (x,y) - The x is the independent (explanatory) variable, the one that you control - Y is the dependent (response) variable Types of Correlation - Positive, as x increases, y increases - Negative, as x increases, y decreases - No correlation - Non Linear Creating on Calculator - Put x data in L1 and y data in L2 - To graph, 2nd -> Y= - Select Plot 1 - Make sure it is on - Make sure X list is in L1, and Y list is in L2 - Select Zoom -> #9 Correlation Coefficient - Measures the type and strength of linear correlation between the two variables - Stat -> Calc -> 2-Var Stats
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