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A guidance counselor claims that high school students in a college preparation program have higher ACT...

A guidance counselor claims that high school students in a college preparation program have higher ACT scores than those in a general program. The sample mean ACT score for 49 high school students who are in a college preparation program is 22.2 and the sample standard deviation is 4.8. The sample mean ACT score for 44 high school students who are in a general program is 20.0 and the sample standard deviation is 5.4.

Use an 8% level of significance to conduct test the guidance counselor’s claim. Assume the distribution of ACT scores for both programs are approximately normally distributed. Assume that σ_{college prep}² ‡ σ_general² .

H₀: Level of significance (α): α =

H_A: Type test: two-tailed left tail right tail

Specify the random variable and distribution to be used in this hypothesis test.

Calculate the p-value Draw a graph and show the p-value

Show your work and any calculator functions used.

Compare the p-value with α Decide to Reject or Fail to reject the null hypothesis

Conclusion. State your results in non-technical terms.

Expert Solution

Let denotes the mean ACT score for high school students who are in a college preparation program and denotes the mean ACT score for high school students who are in a general program.

Level of significance (α): α = 0.08

Type of test : right tail

Conclusion : There is sufficient evidence to support the guidance counselor’s claim that high school students in a college preparation program have higher ACT scores than those in a general program.

milcah answered 1 month ago

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