A college entrance exam company determined that a score of 20 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 250 students who completed this core set of courses results in a mean math score of 20.5 on the college entrance exam with a standard deviation of 3.3. Do these results suggest that students who complete the core curriculum are ready for college-level mathematics? That is, are they scoring above 20 on the math portion of the exam? Complete parts a) through d) below. a) State the appropriate null and alternative hypotheses.
- Given Information :
A college entrance exam company determined that a score of 20 on the mathematics portion of the exam suggests that a student is ready for college-level mathematics. To achieve this goal, the company recommends that students take a core curriculum of math courses in high school. Suppose a random sample of 250 students who completed this core set of courses results in a mean math score of 20.5 on the college entrance exam with a standard deviation of 3.3.
Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
Ho: Average score on the mathematics portion of the exam is equal to 20 .
=
Ha: Average score on the mathematics portion of the exam is above 20 .
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This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.
For a t-test for one mean, the sampling distribution used for the t-test statistic (which is the distribution of the test statistic under the assumption that the null hypothesis is true) corresponds to the t-distribution, with n-1 degrees of freedom
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