In university classes 32 or le

In university classes 32 or less, university students have 50or more
When compared with the classes, it is claimed that they likedmore and got higher grades.
In order to test this claim, the university administration isresponsible for the same lesson, both 32 people small and 50 peoplelarge.
He gave a teacher to give to a class. Same to students in bothclasses at the end of the semester
final exam has been applied. The average score of the largeclass is 72 and the standard deviation is 5, the score of the smallclass
If the average is 75 and the standard deviation is 4, whatresult can be deducted with the level of significance of 0.01, whatis the p value?

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: HA: 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:

 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 ~ tn1 + n2 – 2. Hence, forlevel of significance α%,

p-value = P(tn1 + 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

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