In: Statistics and Probability
For the following cases, you may use either the P-value approach or the rejection region approach to present a full hypothesis test, including:
Let be the the average.ACT scores, scored by all high school college students going through a preparatory program..
Let be the the average.ACT scores scored by high school college students going through a general program..
Given:
For: = 22.2, s1 = 4.8, n1 = 49
For: = 20, s2 = 5.4, n2 = 46
Since s1/s2 = 4.8/9.4= 0.89 (it lies between 0.5 and 2) we used the pooled variance.
The degrees of freedom used is n1 + n2 - 2 = 49 + 46 - 93 (since pooled variance is used)
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The Hypothesis:
H0: =
Ha: >
This is a Right tailed test.
The Test Statistic:
The p Value: The p value (Right Tail) for t = 2.1 , df = 93,is; p value = 0.0191
The Critical Value: The critical value (Right tail) at = 0.05, df = 93, t critical= +1.291
The Decision Rule:If t observed is > t critical, Then Reject H0.
Also If the P value is < , Then Reject H0
The Decision: Since t observed (2.1) is > t critical (1.291), We Reject H0.
Also since P value (0.0191) is < (0.10), We Reject H0.
The Conclusion: There is sufficient evidence at the 90% significance level to support the claim that the high school students in a preparatory program score higher on the ACT than those in in a general program.
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