Ms. Harper knows that her students in a computing course can choose from one of three operating systems for the semester: Doors, Banana, or Duix. Ms. Harper wants to test the hypothesis that her students will select the operating systems in the same proportion as students in other computing courses at the university. She conducts a χ2 goodness-of-fit test and calculates χ2=3.79 with a corresponding p-value of 0.15. Which of the following is correct at a 5-percent level of significance? A) Reject the null hypothesis, since 3.79>2. B) Fail to reject the null hypothesis, since 3.79>2. C) Reject the null hypothesis, since 0.15>0.05. D) Fail to reject the null hypothesis, since 0.15>0.05. E) Reject the null hypothesis, since 0.15<3.790.
Ms. Harper knows that her students in a computing course can choose from one of three operating systems for the semester: Doors, Banana, or Duix. Ms. Harper wants to test the hypothesis that her students will select the operating systems in the same proportion as students in other computing courses at the university. She conducts a χ2 goodness-of-fit test and calculates χ2=3.79 with a corresponding p-value of 0.15. Which of the following is correct at a 5-percent level of significance?
A) Reject the null hypothesis, since 3.79>2.
B) Fail to reject the null hypothesis, since 3.79>2.
C) Reject the null hypothesis, since 0.15>0.05.
D) Fail to reject the null hypothesis, since 0.15>0.05.
E) Reject the null hypothesis, since 0.15<3.790.
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Answer: D) Fail to reject the null hypothesis, since 0.15>0.05.
Explanation: Since the p-value (0.15) is greater than the significance level (0.05), we fail to reject the null hypothesis.
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