In: Math
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 σcollege prep2 ‡ σgeneral2 .
H0: Level of significance (α): α =
HA: 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.
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.