Question

In university classes 32 or less, university students have 50 or more

When compared with the classes, it is claimed that they liked more and got higher grades.

In order to test this claim, the university administration is responsible for the same lesson, both 32 people small and 50 people large.

He gave a teacher to give to a class. Same to students in both classes at the end of the semester

final exam has been applied. The average score of the large class is 72 and the standard deviation is 5, the score of the small class

If the average is 75 and the standard deviation is 4, what result can be deducted with the level of significance of 0.01, what is the p value?

Answer 1

Solution

Let X = score of the large class

      Y = score of the small class

Let mean and standard deviation of X be respectively µ₁ and σ₁ and those of Y be µ₂ andσ₂, where we assume σ₁² = σ₂² = σ², say and σ² is unknown.

Hypotheses:

Null: H₀: µ1 = µ2 Vs Alternative: H_A: µ1 ≠ µ2

Test Statistic:

t = (Xbar - Ybar)/[s√{(1/n₁) + (1/n₂)}]

where

s² = {(n₁ – 1)s₁² + (n₂ – 1)s₂²}/(n₁ + n₂ – 2);

Xbar and Ybar are sample averages and

s₁,s₂ are sample standard deviations based on n₁ observations on X and n₂ observations on Y respectively.

Calculations

Summary of Excel calculations is given below:

n1	50
n2	32
Xbar	72
Ybar	75
s1	5
s2	4
s2	21.5125
s	4.6382
tcal	2.8571
α	0.01
p-value	0.0054

Distribution, Significance Level, α and p-value:

Under H₀, t ~ t_{n1 + n2 - 2}. Hence, for level of significance α%,

p-value = P(t_{n1 + n2 - 2} > | tcal |)

Using Excel Function: Statistical TDIST, this is found to be as shown in the above table.

Decision:

Since p-value < α, H₀ is rejected.

Conclusion:

There is not sufficient evidence to suggest that the two classes have the mean and hence we conclude that large class and small class differ in their mean score. Answer 1

As shown in the table above, p-value = 0.0054  Answer 2

DONE