Question

suppose the following chart gives the grades of 5 students in a past year for their first test and final exam

test 1: A 65. B 74. C 82. D 96. E 18

final : A 80. B 72. C 87. D 99. E 42

does the data suggest that the test scores improved from the first test to the final exam ? set up and test the appropriate hypotheses and use a level of significance of 0.05

Answer 1

Answer)

As the population standard deviation is unknown, we will use two sample t test

First we need to estimate the mean and s.d for both the groups.

Final:

u1 = 76

S1 = 21.436

For test 1

u2 = 67

S2 = 29.6648

N1 = n2 = 5

Test statistics (t) = (u1-u2)/standard error

Standard error = √{(s1^2/n1)+(s2^2/n2)}

After substitution

t = 0.5498645920498

Degrees of freedom is smaller of n1-1,n2-1

In this case df = 4

For df = 4 and test statistics = 0.5499

Required p-value is = 0.305856

As the obtained p-value is greater than the given significance level of 0.05

We fail to reject the null hypothesis

And we do not have enough evidence to support the claim that the scores have improved.