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A math teacher tells her students that eating a healthy breakfast on a test day will help their brain function and perform well on their test. During finals week, she randomly samples 45 students and asks them at the door what they ate for breakfast. She categorizes 25 students into Group 1 as those who ate a healthy breakfast that morning and 20 students into Group 2 as those who did not. After grading the final, she finds that 48% of the students in Group 1 earned an 80% or higher on the test, and 40% of the students in Group 2 earned an 80% or higher. Can it be concluded that eating a healthy breakfast improves test scores? Use a 0.05 level of significance.
Hypotheses:
H0: p1 = p2
H1: p1 > p2
In this scenario, what is the p-value? (Round to 4 decimal places)
p-value =
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Assuming the population of times is normally distributed, and using the 0.05 level of significance, should we conclude that the new booklet is effective? Determine and interpret the p-value for the test.
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