Statistical Analysis of Weight, Test Scores, Training Methods, and Road Traffic Data

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Question One
a. Stating the hypotheses to determine if there is a significant difference between the
weights of the contestants before and after the first week of the programme.
The hypotheses are
H0 : μ0=μ1
H1=μ0 ≠ μ1
b. Computation of test statistic to test the hypotheses
Here the t statistic (paired test) will be applied
t= ∑ D
√ n ∑ D2− (∑ D )2
n−1
w h ere t h e D=difference between X∧Y ,n=sample ¿ 12
In this case, the degree of freedom will be given by n−1=12−1=11
Column1 Before Program(kg)(X)
Weight week 1(Kg)
(Y) D =X-Y D^2
89 88 1 1
67 66.5 0.5 0.25
112 110.5 1.5 2.25
109 108.5 0.5 0.25
56 55.5 0.5 0.25
123.5 119 4.5 20.25
108 106.5 1.5 2.25
73 72.5 0.5 0.25
83 82 1 1
94.5 95 -0.5 0.25
78.5 78.5 0 0
65 63.5 1.5 2.25
n(sample size) 12 12
means 88.2083 87.1667
Sum ( D and D^2) 12.5 30.25

Therefore,
t= 12.5
√ 12 ( 30.5 )−12.52
12−1
= 12.5
√ 363−156.25
11
¿ 12.5
√ 206.75
11
= 12.5
4.3354
¿ 2.8833
Hence, tcomputed=2.8833
c. Specification and justification of an appropriate probability for committing
Type I error (α)
The probability of committing type I error will be 5%, which is the probability of
incorrectly rejecting the null hypothesis. This will be attained at the significance level
of 95%, which is the probability of rejecting or accepting the null hypothesis
accurately.
To make the decision, in this case, the critical value of need to determine from
t-tables
t0.05 ( 11df ) ( twotailed ) =1.796
d. Reporting of the decision and clearly explain your result.
The tcomputed=2.8833 ¿ tα =1.796 , therefore, null hypothesis,H0 t h e t h e t h e : μ0=μ1
is rejected. This suggest that there is significant difference between the weights
of the contestants before and after the first week of the programme .

In this case, alternative hypothesis H1=μ0 ≠ μ1 is accepted. In conclusion the
weight of the contestant is not the same before and after the programme, the t-
test conducted reveals this.
Question Two
a. Stating the hypotheses determine if there is a significant difference between the test
scores of both classes
The hypotheses to be determined are
H0 : μ0=μ1
H1=μ0 ≠ μ1
b. Calculation of test statistic to test the hypotheses
Due to an unequal sample size of the two variables, t-statistics (unpaired test), equal
variance, will be conducted.
t= ( X −Y )
√ ( sx
2
n1
+ sy
2
n2 )
where , s x
2∧s y
2 are the variance of X∧Y respectively , X∧Y are the means of X
Y are the means of X∧Y respectively , n1∧n2 are the sample ¿ X a nd Y