Statistical Reasoning in Psychology

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Statistical Reasoning in Psychology 1. A prison psychologist recorded the number of rule infractions for 15 prison inmates over a six - month period to be 5, 4, 2, 4, 3, 5, 2, 0, 4, 4, 5, 5, 3, 4, and 3. a. Make a frequency table. number Tally frequency 0 – 2 / 1 2 – 4 // /// 5 4 – 6 ///////// 9 b. Make a histogram based on the frequency table.
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c. Describe in words the shape of the histogram. The histogram depicts that the shape of the distribution is left - skewed . 2. Identify and solve this problem by hand. The head of public safety notices that the average driving speed at a particular intersection averages μ = 35 mph with a standard deviation of σ = 7.5 mph. After a school speed limit sign of 20 mph is p laced at the intersection, the first 40 cars travel past at an average speed of 32 mph. Using the .01 significance level, was there a significant change in driving speed? Answer: a. Null hypothesis, H0: μ = 35 Alternative hypothesis, H1: μ ≠ 35 Test statis tic: z = sqrt (n)*(xbar – μ )/ σ which under the null hypothesis follows a standard normal distribution. Critical region: Reject H0 iff the test statistic is greater than 2.5 8 or the test statistic is less than – 2.5 8 (point on a standard normal distribution above which 0.5% of the d istribution lies) . Calculation: n = 40 σ = 7.5 xbar = 32 Test statistic , z = sqrt (40)*(32 – 35)/7.5 = – 2.5 3

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