A sample of scores on an examination given in two different classes is examined.
ID: 3232898 • Letter: A
Question
A sample of scores on an examination given in two different classes is examined. The following Excel output was obtained.
t-Test: Two-Sample Assuming Unequal Variances
class 1
class 2
Mean
78
79
Variance
90
47.333
Observations
9
7
Hypothesized Mean Difference
0
df
14
t Stat
-0.244
P(T<=t) one-tail
0.405
t Critical one-tail
1.761
P(T<=t) two-tail
0.811
t Critical two-tail
2.145
a) Use = .05. In order to determine if Class 2 has a different grade from Class 1, what are the null and alternative hypotheses?
b) Use = .05. Exactly what p-value did you use to answer to determine if Class 2 has a different average?
c) Use = .05. Does Class 2 have a different grade?
t-Test: Two-Sample Assuming Unequal Variances
class 1
class 2
Mean
78
79
Variance
90
47.333
Observations
9
7
Hypothesized Mean Difference
0
df
14
t Stat
-0.244
P(T<=t) one-tail
0.405
t Critical one-tail
1.761
P(T<=t) two-tail
0.811
t Critical two-tail
2.145
Explanation / Answer
Solution:-
a)
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 = 2
Alternative hypothesis: 1 2
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
b) This is two tailed test so p-value that we use to answer to determine if Class 2 has a different average is 0.811.
c) Since 0.811 is greater than the significance level 0.05, hence we have to accpet the null hypothesis.
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