Statistics Assignment

Statistics
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Statistics
Elementary statistics
Question 1
The table below represents the maximum and minimum value of math4 (percentage students
passing meap math) and the range computed from it.
Maximum math4 100
Minimum math4 0
Range 100
The above range indicates that there is great variability in math4. This indicated that the
difference between the smallest and largest value was too large.
From the data that was provided the schools that had a perfect pass rate in math test were 1664.
This indicated that more schools recorded a perfect pass in the math test. The number of schools
that recorded a great pass in math scores was equivalent to 91.28%. The number of schools that
had exactly a pass of exactly 50% in math test was 17 which was equivalent to 0.93%.
The following hypothesis was used to compare whether the average pass rate for math and
reading scores are different from each other.
H0: the average pass rate for math and reading scores was the same
Versus
H1: the average pass rate for math and reading scores are different
An independent t-test was performed and the test was performed at a 5% level of significance.
The following is the output of the test.
math4 read4
Mean 71.909
60.0618
8
Variance
398.165
8
366.618
8
Observations 1823 1823

Statistics
Pooled Variance
382.392
3
Hypothesized Mean
Difference 0
df 3644
t Stat
18.2909
6
P(T<=t) one-tail 7.11E-72
t Critical one-tail
1.64527
2
P(T<=t) two-tail 1.42E-71
t Critical two-tail
1.96061
5
The test had a p-value of 1.42e-71 which is less than 5% level of significance this lead to the
rejection of the null hypothesis (Thapa et al, 2012). This lead to the conclusion that the average
pass rate for math and reading scores are different. The math test was harder than the reading test
and the average mean difference was 11.85.
The table below represents the correlation coefficient between math4 and read4
math4 read4
math4 1 0.842728
read4 0.842728 1
The correlation coefficient between the math4 and read4 was 0.84 this indicated evidence of a
strong positive correlation between the two variables.
The table below represents the average and standard deviation of exppp.
Average 5194.86
Standard deviation 1091.89
This standard deviation indicated that the observation was 1091.89 times about the mean.
compared with the mean of exppp, the standard deviation shows that there was no greater
variability in the observation of exppp.