Population mean or mean score of school

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STATISTICS
Name of the Student
Name of the University
Author Note
STATISTICS1
1.
The null hypothesis of the research is
H0: The mean exam score of the class is less or equal to than the school average score.
The research hypothesis or alternative hypothesis is
H1: The mean exam score of the class is greater than school average score.
Given, sample size n = 20
Mean average of class or sample mean xbar = 80
Population mean or mean score of school μ= 70
Sample standard deviation s = 10
As, the population standard deviation is unknown, hence t test is applied assuming the
population is approximately normally distributed. The t test will be a right tailed from the
alternative hypothesis.
Test statistics t = (xbar – μ)/(s/sqrt(n)) = (80 – 70)/(10/sqrt(20)) = 4.47.
xbar 80
μ 70
s 10
n 20
Standard
error
2.236068
t stat 4.472136
p value 0.000131
Decision Reject the
STATISTICS2
null
hypothesis
as p value
less than
0.05
Hence, the null hypothesis is rejected at significance level of 5% as the p value is less than
the considered significance level. Thus it can be concluded that there is sufficient evidence to
reject the null hypothesis and state the mean exam score of the class is greater than school
average score.
2.
Null hypothesis (H0): The mean exam score of the class is same as school average score of
exam.
Alternative or research hypothesis (H1): The mean exam score of the class is significantly
different from the school average score of the exam.
Given, sample size n = 20
Mean average of class or sample mean xbar = 80
Population mean or mean score of school μ= 60
Sample standard deviation s = 10
As, the population standard deviation is unknown, hence t test is applied assuming the
population is approximately normally distributed. The t test will be a two tailed test from the
alternative hypothesis.

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