Answer:
b
Step-by-step explanation:
We will conduct a hypothesis test for dependent samples since the same subjects were retested.
We first need to find the difference in scores
Student 1: 450 - 440 = 10
Student 2: 520 - 600 = -80
Student 3: 720 - 720 = 0
Student 4: 600 - 630 = -30
Now find the mean of the differences: d = (10 - 80 + 0 - 30)/4 = -100/4 = -25
Now find the standard deviation, which is the square root of the variance:
[(10 - (-25))² + (-80 - (-25))² + (0 - (-25))² + (-30 - (-25))²]/(4*3) =
[35² + (-55)² + 25² + (-5)²]/12 = 4900/12 = 408.3333
s = √(4900/12) = 20.2073
Find the test statistic: t = (d - µ)/(s/√n)
t = (-25 - 0)/(20.2073/√4) = -2.474
For a critical region of this two tailed test, for a 90% significance level, we get a t-value of: t < -2.353 or t > 2.353, since our test statistic is in this region, b is a valid answer
For a critical region of this two tailed test, for a 99% significance level, we get a t-value of: t < -5.841 or t > 5.841, since our test statistic isn't in this region, c is not a valid answer
