Question

a college entrance exam company determined that a score of 24 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 24.6 on the college entrance exam with a standard deviation of 3.7. do these results suggest that students who complete the core curriculum are ready for college - level mathematics? that is, are they scoring above 24 on the mathematics portion of the exam? complete parts a) through d) below.
d. a boxplot of the sample data shows no outliers
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 } = 2.56 \\) (round to two decimal places as needed)
identify the p - value
p - value \\( = 0.006 \\) (round to three decimal places as needed)
d) write a conclusion based on the results. choose the,correct answer below.
the null hypothesis and claim that there sufficient evidence to conclude that the population mean is than 24.

Explanation:

Step1: Compare P - value and significance level

The significance level is \(\alpha = 0.10\). The P - value is \(0.006\).
Since \(P - value=0.006<\alpha = 0.10\).

Step2: Make a decision about the null hypothesis

When \(P - value<\alpha\), we reject the null hypothesis.
The null hypothesis is \(H_{0}:\mu = 24\) and the alternative hypothesis is \(H_{1}:\mu>24\) (because we want to know if they are scoring above 24).

Answer:

Reject the null hypothesis and claim that there is sufficient evidence to conclude that the population mean is greater than 24.