Statistics Exam: Frequency Distribution, Regression Analysis, ANOVA, and Sales Data

Statistics
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Question 1 (7 marks)
Below you are given the examination scores of 20 students (data set also provided
in
accompanying MS Excel file).
a. Construct a frequency distribution, cumulative frequency distribution, relative
frequency distribution, cumulative relative frequency distribution and percent
frequency distribution for the data set using a class width of 10. (5 marks)
Answer
Class Frequency Cumulative
frequency
Relative
frequency
Cumulative relative
frequency
Percent
frequency
50-59 3 3 0.15 0.15 15%
60-69 2 5 0.1 0.25 25%
70-79 5 10 0.25 0.5 50%
80-89 4 14 0.2 0.7 70%
90-99 6 20 0.3 1 100%
b. Construct a histogram showing the percent frequency distribution of the
examination
scores. Comment on the shape of the distribution. (2 marks)
Answer
The shape of the histogram shows a kind of left skewed distribution, this shows that the
distribution is negatively skewed. However, the skewness is not severe.

Question 2 (8 marks)
Shown below is a portion of a computer output for a regression analysis relating supply (Y in thousands
of units) and unit price (X in thousands of dollars)
a. What has been the sample size for this problem? (1 mark)
Answer
Sample size = 39+1+1 = 41
b. Determine whether or not supply and unit price are related. Use α = 0.05. (2 marks)
Answer
We obtain the t-value
tvalue= Beta
Standard Error = 0.029
0.021 =1.3810
The t-critical value is 2.022; this value is greater than the computed value hence the null
hypothesis is not rejected. This means that supply and unit price are not related at α = 0.05.
c. Compute the coefficient of determination and fully interpret its meaning. Be very specific. (2
marks)
Answer
R2= EE
TSS = 354.689
354.689+7035.262 = 354.689
7389.951 =0.047996
The coefficient of determination is 0.048; this implies that unit price only explains 4.8% of the
variation in the dependent variable.
d. Compute the coefficient of correlation and explain the relationship between supply and unit
price. (2 marks)
Answer
Coefficient of correlation= √ R2=R
Coefficient of correlation= √0.047996=0.2191
The coefficient of correlation is 0.21921; this indicates that there is a weak positive relationship
between supply and unit price.
e. Predict the supply (in units) when the unit price is $50,000. (1 mark)
Answer
The regression equation model is;
y=54.076 +0.029( X)
So when X =$ 50,000
Supply would be;