Question

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?

Answer 1

To test the claim that the average age of students at Gorka College is greater than the average age of students at Yapoah College, a t-test is used. The calculated t-statistic is 1.363, the degrees of freedom using the conservative method is 97, and the p-value is greater than 0.05. Therefore, there is not enough evidence to support the claim.

Step-by-step explanation:

To test the claim that the average age of students at Gorka College is greater than the average age of students at Yapoah College, we can use a t-test. The t-statistic is calculated by subtracting the mean of Yapoah College from the mean of Gorka College and dividing it by the standard error of the difference between the means. In this case, the t-statistic is (21.2 - 20.7) / sqrt((1.1^2 / 53) + (1.2^2 / 46)) = 1.363.

The degrees of freedom, using the conservative method, is calculated as (53 - 1) + (46 - 1) = 97. The p-value for the t-statistic can be looked up in a t-table using the degrees of freedom and the t-value. If we look up the critical value for a one-tailed test with 97 degrees of freedom and a significance level of 0.05, we find it to be approximately 1.66. Since the t-statistic of 1.363 is less than the critical value, the p-value is greater than 0.05.

Therefore, the p-value is greater than the significance level of 0.05. This means that there is not enough evidence to support the claim that the average age of Gorka College students is higher than for Yapoah College students.

Answer 2

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.