Question

A college entrance exam company determined that a score of 2222 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 150150 students who completed this core set of courses results in a mean math score of 22.722.7 on the college entrance exam with a standard deviation of 3.93.9. Do these results suggest that students who complete the core curriculum are ready for​ college-level mathematics? That​ is, are they scoring above 2222 on the math portion of the​ exam? Complete parts​ a) through​ d) below.

Answer 1

Answer:

Yes, Students are scoring above 2222 on the math portion of the​ exam.

Step-by-step explanation:

We are given that a college entrance exam company determined that a score of 2222 on the mathematics portion of the exam suggests that a student is ready for​ college-level mathematics i.e., population mean is 22.

Null Hypothesis, $H_0$ : $\mu$ = 22 {Students are scoring equal to 2222 on the math portion of the​ exam}

Alternate Hypothesis, $H_0$ : $\mu$ > 22 {Students are scoring above 2222 on the math portion of the​ exam}

Also, a random sample of 150 students who completed this core set of courses results in a mean math score of 22.7 on the college entrance exam with a standard deviation of 3.93 i.e.;

Sample mean, $Xbar$ = 22.7    and Sample standard deviation, s = 3.93

The Test statistics is given by;

                            Z = $\frac{Xbar -\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

Test Statistics = $\frac{22.7 -22}{\frac{3.93}{\sqrt{150} } }$ ~ $t_1_4_9$

                        = 2.1815

Since, we are not given with the significance level, so we assume it to be 5%. At 5% significance level t table gives critical value of 1.6578 at 149 degree of freedom. Since our test statistics is more than the critical value so we reject null hypothesis as our test statistics fall in the rejection region.

Therefore, we conclude that Students are scoring above 2222 on the math portion of the​ exam.