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Statistical Reasoning in Psychology

This assignment solution covers statistical reasoning techniques used in psychological research.

Benjamin Fisher
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Statistical Reasoning in Psychology1. A prison psychologist recorded the number of rule infractions for 15 prisoninmates 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.numberTallyfrequency0–2/12–4/////54–6/////////9b.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 particularintersection averagesμ= 35 mph with a standard deviation ofσ= 7.5 mph. After aschool speed limit sign of 20 mph is placed at the intersection, the first 40 cars travelpast at an average speed of 32 mph. Using the .01 significance level, was there asignificant change in driving speed?Answer:a.Null hypothesis,H0:μ= 35Alternative hypothesis, H1:μ≠35Test statistic:z =sqrt(n)*(xbar–μ)/σwhich under the null hypothesis follows a standard normal distribution.Critical region: Reject H0 iff the test statistic is greater than 2.58or the test statisticis less than–2.58(point on a standard normal distributionabove which 0.5% of thedistribution lies).Calculation: n=40σ= 7.5xbar = 32Teststatistic, z=sqrt (40)*(32–35)/7.5 =–2.53
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