PS390 Statistical Reasoning in Psychology Assignment 04

ASSIGNMENT 04
PS390 Statistical Reasoning in Psychology
Student Name:
Instructor Name:
Course Number:
20th August 2018
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1. (25 points) 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.
Answer
Class Frequency
0 1
2 2
3 3
4 5
5 4
b. Make a histogram based on the frequency table.
Answer
c. Describe in words the shape of the histogram.
Answer
The shape of the histogram shows that the data is not normally distributed but is
rather skewed to the left (longer tail to the left)
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2. (25 points) 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 placed 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?
a. Use the five steps of hypothesis testing (report results in APA format).
Answer
Step 1: State the null hypothesis and the alternate hypothesis
The hypothesis to be tested in this case is;
H0 : μ=35
H A : μ ≠ 35
Step 2: Select the appropriate test statistic and level of significance
The test statistic for this problem would be the z-score
Z= x−μ
σ / √n
The level of significance is 0.01 (i.e. α = 0.01)
Step 3: State the decision rules
The critical z value is 2.576. This means that the null hypothesis is rejected if the
computed z-score value is greater than the critical z-value. Otherwise we fail to reject
the null hypothesis.
Step 4: Compute the appropriate test statistic and make the decision
Z= x−μ
σ / √n = 32−35
7.5/ √40 =−2.52982
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|Z|=|−2.52982|=2.52982
The computed Z score (absolute value) is 2.52982; this value is less than the critical
z-value of 2.576. This means that we do not reject the null hypothesis.
Step 5: Interpret the decision
By not rejecting the null hypothesis we conclude that there is no significant change in
driving speed at 1% level of significance.
b. Sketch the distributions involved.
c. Figure the confidence limits for the 99% confidence interval.
Answer
The confidence interval (C.I) is given as;
C . I : x ± ME
ME=
z α
2
σ
√n = 2.576∗7.5
√40 =3.05476
x=32
C . I : x ± ME →32 ± 3.05476
Lower limit: 32−3.05476=28.94524
Upper limit: 32+3.05476=35.05476
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