In university classes 32 or le

Solution

Let X = score of the large class

      Y = score of the small class

Let mean and standard deviation of X be respectivelyµ₁ and σ₁ and those of Y be µ₂andσ₂, where we assume σ₁²= σ₂² = σ², say and σ²is unknown.

Hypotheses:

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

TestStatistic:

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 basedon n₁ observations on X and n₂ observationson Y respectively.

Calculations

Summary of Excel calculations is given below:

Distribution,Significance Level, α and p-value:

Under H₀, t ~ t_{n1 + n2 – 2}. Hence, forlevel of significance α%,

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

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

Decision:

Since p-value < α, H₀ is rejected.

Conclusion:

There is not sufficient evidence to suggest that the two classeshave the mean and hence we conclude that large class andsmall class differ in their mean score. Answer1

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

DONE