Question

In: Statistics and Probability

For the following cases, you may use either the P-value approach or the rejection region approach...

For the following cases, you may use either the P-value approach or the rejection region approach to present a full hypothesis test, including:

  1. Identifying the claim and H0 and Ha,
  2. Finding the appropriate standardized test statistic,
  3. Finding the P-value or the rejection region,
  4. Deciding whether to reject or fail to reject the null hypothesis, and
  5. Interpreting the decision in the context of the original claim.
  1. A guidance counselor claims that high school students in a college preparatory program score higher on the ACT test than those in a general program.  The mean ACT score for a random sample of 49 students in the college preparatory program is 22.2 with a standard deviation of 4.8.  The mean ACT score for a random sample of 46 students in the general program is 20.0 with a standard deviation of 5.4.  Perform the appropriate test on the counselor’s claim with regard to the difference between the mean ACT scores at α = 0.10.

Solutions

Expert Solution

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)

________________________________________

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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