The teacher of a class of 40 high school seniors is curious

The teacher of a class of 40 high school seniors is curious whether the mean Math SAT score ? for the population of all 40 students in his class is greater than 500 or not. To investigate this, he decides to test the hypotheses

H₀: ? = 500         H_a: ? > 500

Select one or more:

a. H₀ cannot be rejected at level ? = 0.05 because 500 is within confidence interval.

b. H₀ cannot be rejected at level ? = 0.05, but this must be determined by carrying out the hypothesis test rather than using the confidence interval.

c. We can be certain that H₀ is not true.

Solution

OPTION A: H0 cannot be rejected at level = 0.05 because 500 is within confidence interval. [ANSWER]

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The confidence interval is 502+/-31, or (471, 533), which indeed includes 500. Hence, the answer is OPTION A.

As to options B and C, we can actually use confidence intervals. However, we cannot be \"certain\", we can only be \"confident\".