A group of 5 statistics students receive the following grades on a test: 81, 74,

Question

A group of 5 statistics students receive the following grades on a test: 81, 74, 62, 92, and 76. An intervention plan is used and the students increased their scores on a retest to: 89, 78, 59, 98 and 75. At the 0.025 significance level, is the intervention plan helpful in increasing the grades?

a. State the null and alternate hypotheses Ho : H1:

b.State the decision rule.

c. Compute the value of the test statistic.

d. Estimate the p-value.

e. What is your decision regarding the null hypothesis? Interpret the result.

Explanation / Answer

Set up Hypothesis
Null Ho: Ud = 0
Alternate,the intervention plan helpful in increasing the grades H1: Ud < 0
Test Statistic
to= d/ (S/n)
Where
Value of S^2 = [ di^2 – ( di )^2 / n ] / ( n-1 ) )
d = ( Xi-Yi)/n) = -2.8
We have d = -2.8
Pooled variance = Calculate value of Sd= S^2 = Sqrt [ 126-(-14^2/5 ] / 4 = 4.66
to = d/ (S/n) = -1.34
Critical Value
The Value of |t | with n-1 = 4 d.f is 2.776
We got |t o| = 1.34 & |t | =2.776
Make Decision
Hence Value of |to | < | t | and Here we Do not Reject Ho

We don't have evidence that the intervention plan helpful in increasing the grades

X Y X-Y (X-Y)^2 81 89 -8 64 74 78 -4 16 62 59 3 9 92 98 -6 36 76 75 1 1 -14 126

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