(Solved): A college entrance exam company determined that a score of 25 on the mathematics portion of the exa ...

A college entrance exam company determined that a score of 25 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 250 students who completed this core set of courses results in a mean math score of \( 25.4 \) 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 25 on the mathematics portion of the exam? Complete parts a) through d) below a) State the appropriate null and alternative hypotheses. Fill in the correct answers below. The appropriate nuil and alternative hypotheses are \( \mathrm{H}_{0} \) versus \( \mathrm{H}_{1} \) : b) Verily that the requirements to perform the test using the t-distribution are satisfied. Check all that apply A. The sample size is larger than 30 . B. A boxplot of the sample data shows no outliers. C. The sample data come from a population that is approximately normal. D. The students were randomly sampled. E. The students' test scores were independent of one another. F. None of the requirements are satisfied c) Use the P-value approach at the \( \alpha=0.10 \) level of significance to test the hypotheses in part (a) Identify the test statistic \( t_{0}= \) (Round to two decimal places as needed) Identify the P-value. P.value = (Round to three decimal places as needed) d) While a conclusion based on the results. Choose the correct answer bolow. the null hypothesis and claim that there sufficient evidence to condude that the population mean is than 25 .