Statistics HW_Ch 7_Hypothesis z Testing (1)

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University of Texas, Rio Grande Valley *

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Economics

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Feb 20, 2024

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1. The average age of licensed drivers in a county is = 38, σ (standard deviation) = 10, and the distribution is approximately normal. A county police officer was interested in whether the average age of drivers receiving parking tickets differed from the average age of the driving population. She obtained a sample of N = 30 drivers receiving parking tickets. The average age of these drivers was M = 42. Perform the six steps of hypothesis testing necessary to determine whether this group differs from the population of drivers in the county. Six steps of hypothesis testing Step 1: Populations, Distribution, and Assumptions Population 1: Drivers and their average age Population 2: Drivers and their average age throughout the county Distribution: Distribution of means Assumptions (Explain): 1. The dependant variable is on a set scale 2. participants were not randomly selected and were selected based on whether or not they recieved a ticket 3. Ditribution is approximately normal, and the sample size is 30 Step 2: Hypotheses Research hypothesis: Parking tickets correlate to a specific age group of licensed drivers Symbolic: H1: μ1 ≠ μ2 (not sure to correctly input subscript) Null hypothesis: Parking tickets do not correlate to a specific age group of licensed drivers Symbolic: H1: μ1 = μ2 Step 3: Characteristics of the Comparison Distribution μ M = ____38___________ σ M = ______10_________ M = _______42________ N = _______30________

Step 4: Critical Values p level = ______0.05___5%______ ____2_____ -tailed test Critical values (i.e., cutoffs) is/are = _______-1.96________1.96_______________ Step 5: Calculate the test statistic (show your work) z = ______0.4_________ Used z score chart to find 2.5% split between both tails (1.96) (42-38)/10 = 0.4 Step 6: Make a Decision (Explain) 0.4 z score falls between the critical values meaning there is no evidence to support the research hypothesis, so we fail to reject the null hypothesis.

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