14 Oct Central Limit Theorem
Complete the following problems within the Word document (do not submit other files). Show your work for problem sets that require calculations. Ensure that your answer to each problem is clearly visible.(You may want to highlight your answer or use a different type of color to set it apart.)
Problem Set 3.1: Central Limit Theorem
• Criterion: Determine if a distribution will be normally distributed based on sample size.• Data: As part of a large research study, you administer a new test to 20,000 adults.• Instruction: Answer the following:o Before you record or analyze the data, can you assume that the sampling distribution of the mean for this test will be normally distributed?o Why or why not?
Problem Set 3.2: Standard Error of the Mean
• Criterion: Calculate the standard error of the mean.• Data: College students in a large psychology class take a final exam. The mean exam score is 85, and the standard deviation is 5.• Instruction: Using the formula for σM, what will the standard error of the mean (σM ) be when:
a. The sample size is 25.
b. The sample size is 16.
c. The sample size is 20.
Problem Set 3.3: z Test
• Criterion: Calculate a z test to make a decision about a sample.• Data: The average (mean) height for adult women is 65 inches, and the standard deviation is 3.5 inches. Given the women you know, you think this number is low; so, you record the heights of 25 of your female friends. The average height of your 25 friends is 66.84 inches.
Portion of the Normal Curve Table
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