ACC Statistics Notes - Full Hypothesis Test Example (Proportion)

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1. The proportion of all students worldwide who scored a 5 on the AP Statistics exam in 2010 was 0.15 . A study was conducted to measure the effects of cash incentives, in which 17 of the 70 students who were offered cash incentives scored a 5 on the exam. Is there statistically significant evidence that the proportion of students who would score a 5 on the AP Statistics exam would be higher than 0.15 with cash incentives? Assume it is reasonable to use a Normal distribution for the p-value. a. State hypotheses: i. H 0 : p = 0.15 (the default position; what we assume is true) ii. H a : p > 0.15 (what we are testing) b. Calculate the sample statistic: i. = 17/70 c. Identify these values: i. n = sample size: 70 ii. p null = 0.15 d. Determine if it is reasonable to use a Normal distribution for these values of n and p null: i. np = (70)(0.15) = 10.5 ii. n(1 - p) = 70(1 - 0.15) = 59.5 iii. Since the values of np and n(1 - p) > 10, yes , it is reasonable to use a Normal distribution e. Calculate the standard error to four decimal places (formula: SE p = sqrt [ p(1 - p) / n ]) i. SE p = sqrt [ 0.15(1 - 0.15) / 70 ] ; SE p = 0.0427 f.
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