You want to test the claim that the average age of students at Gorka College is greater than the average age of students at Yapoah College. You take a simple random sample of 53 people from Gorka and compute an average age of 21.2 (years) and a standard deviation of 1.1. Then you take a simple random sample of 46 students from Yapoah College and compute an average age of 20.7 and a standard deviation of 1.2.
Compute the t-statistic for testing the alternative hypothesis that the average age of Gorka students is greater than the average age of Yapoah students (set things up so that t is positive).
What are the degrees of freedom (using the conservative method)?
What is the P-value?
Is there significant evidence at the 0.05 level to support the hypothesis that the average age of Gorka students is higher than for Yapoah?

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fichoh fichoh · Answer 1 · 2021-06-16T08:38:45+02:00

Answer:

Kindly check explanation

Step-by-step explanation:

The hypothesis :

H0 : μ1 = μ2

H1 : μ1 > μ2

Given :

x1 = 21.1 ; n1 = 53 ; s1 = 1.1

x2 = 20.7 ; n2 = 46 ; s2 = 1.2

The test statistic :

(x1 - x2) / √[(s1²/n1 + s2²/n2)]

(21.1 - 20.7) / √[(1.1²/53 + 1.2²/46)]

0.4 / 0.2326682

Test statistic = 1.719

The degree of freedom using the conservative method :

Comparing :

Degree of freedom = n - 1

Degree of freedom 1 = 53 - 1 = 52

Degree of freedom 2 = 46 - 1 = 45

Smaller degree of freedom is chosen ;

The Pvalue from Test statistic, using df = 45

Pvalue = 0.0462

Pvalue < α ; Hence, there is significant evidence to conclude that average age of Gorka student is higher than Yaphoa.