Researchers have claimed that the average number of headaches per student during a semester of Statistics is 11. In a sample of n = 16 students the mean is 12 headaches with a deviation of 2.4. Which of the following represent the null and alternative hypotheses necessary to test the students' belief? A) H0: μ = 11 vs. Ha: μ > 11 B) H0: μ = 11 vs. Ha: μ < 11 C) H0: μ < 11 vs. Ha: μ = 11 D) H0: μ = 11 vs. Ha: μ ≠ 11

Question

Mathematics

Shyann

1 February, 17:00

Researchers have claimed that the average number of headaches per student during a semester of Statistics is 11. In a sample of n = 16 students the mean is 12 headaches with a deviation of 2.4. Which of the following represent the null and alternative hypotheses necessary to test the students' belief? A) H0: μ = 11 vs. Ha: μ > 11 B) H0: μ = 11 vs. Ha: μ < 11 C) H0: μ < 11 vs. Ha: μ = 11 D) H0: μ = 11 vs. Ha: μ ≠ 11

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Imogen · Answer 1

A) H0: μ = 11 vs. Ha: μ > 11

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

Therefore, for the case above;

The null hypothesis is that the average number of headaches per student during a semester of Statistics is 11.

H0: μ = 11

The alternative hypothesis is that the average number of headaches per student during a semester of Statistics is greater than 11.

Ha: μ > 11