Question

Northwood and Eastwood are rival schools that wish to compare how their students did in a math competition. 72 randomly chosen Northwood students participated and received a mean score of 28 with a standard deviation of 8, 98 randomly chosen Eastwood students participated and received a mean score of 25 with a standard deviation of 10.

-I got the test statistic, but get lost when calculating the p-value and the degrees of freedom.

(a) The Eastwood math teacher wants to show through statistics that her students receive a higher mean score in the contest. State her hypotheses.

(b) Compute the test statistic and p-value for this test.

(c) Reach your conclusion at the 0.05 significance level. Be sure to interpret in the context of the problem.

(d) In a separate test, the Eastwood teacher finds evidence that Eastwood students performed better than Southwood students. Would this prove that the Eastwood teacher was more effective than the Southwood teacher? Explain briefly.

Answer 1

a) The Eastwood math teacher wants to show through statistics that her students receive a higher mean score in the contest. State her hypotheses.

Given,

Northwood			Eastwood
n1	x1_Bar	s1			n2	x2_Bar	s2
72	28	8			98	25	10

Set Hypothesis:

H0: Eastwood students and Northwood student are equal mean score in the contest.

HA: Eastwood students receive a higher mean score than Northwood student in the contest.

(b) Compute the test statistic and p-value for this test.

Given,

Northwood			Eastwood
N1	x̄1	S1			N2	x̄2	S2
72	28	8			98	25	10

Test Statistics:

P-Value: (by using excel)

Claculate P-Value with (N1+N2-2 = 168) df, α= 0.05 and One tailed test (our alternative hypothesis is one sided) by using excel function TDIST(2.09,168,1) is,

P-Value= 0.019

(c) Reach your conclusion at the 0.05 significance level. Be sure to interpret in the context of the problem.

Decision: P-Value (0.019) is less than 0.05 then we reject H0

Conclusion: We have sufficient evidance to conclude that Eastwood students receive a higher mean score than Northwood student in the contest

(d) In a separate test, the Eastwood teacher finds evidence that Eastwood students performed better than Southwood students. Would this prove that the Eastwood teacher was more effective than the Southwood teacher? Explain briefly.

We have 2 scenarios

1)Eastwood Student performance is good becouse Eastwood teacher was more effective than s outhwood teacher .

2)Eastwood Student performance is good than Southwood and Northwood Student because they intelligent itself (not becouse of teacher)

Yes we can prove that the Eastwood teacher was more effective than the Southwood teacher by scenario 1 only.