(8 points) A guidance counselor claims that high school students in a college pr

Question

(8 points) A guidance counselor claims that high school students in a college prep program have higher ACT scores than those in a general program. The mean ACT score for 25 high school students who are in a college prep program is 22.2, with a standard deviation of 4.8. The mean ACT score for 23 high school students who are in a general program is 20.0, with a standard deviation of 5.4. Assume both populations are normally 11· distributed. a. If the standard deviations above are population standard deviations, analyze the guidance counselor's claim at = 0.10. b. If the standard deviations above are sam ple standard deviations, analyze the guidance counselor's claim at = 0.10.

Explanation / Answer

a)

p-value = 0.0685

As p-value is less than the significance level of 0.10, we reject null hypothesis. There are signifcant evidence to conclude that prep program has higher ACT score than general.

b)

p-value = 0.0721

As p-value is less than the significance level of 0.10, we reject null hypothesis. There are signifcant evidence to conclude that prep program has higher ACT score than general.

Given Data Sample 1 Sample 2 Name Prep General mean 22.2 20 Sample size 25 23 Std. dev. 4.80 5.40

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