Question

The National Assessment of Educational Progress (NAEP) gives a math assessment every year to 12th graders in the U.S. On the math test, a score above 275 indicates that a student has the skills to balance a checkbook. For a random sample of 500 young men, the mean NAEP math score is 272 with a standard deviation of 78. Do we have evidence to support the claim that young men nationwide have a mean score below 275? The null and alternative hypotheses are H 0: μ = 275, H a: μ < 275. The level of significance is 5%. The t-test statistic is −0.86 with a P-value of 0.20. What is the correct conclusion? Group of answer choices The evidence suggests that young men nationwide have a mean score less than 275. We do not have enough evidence to conclude that the mean score is less than 275 for young men nationwide. The evidence suggests that young men nationwide have a mean score equal to 275. It is likely that these 500 young men have a mean score less than 275.

Answer 1

Answer:

The correct answer is option 2.

Step-by-step explanation:

In this case we need to test whether young men nationwide have a mean score below 275 in the National Assessment of Educational Progress math assessment.

The hypothesis is defined as follows:

H₀: μ = 275 vs. Hₐ: μ < 275

The significance level of the test is α = 0.05.

The p-value of the test is computed as, p-value = 0.20.

Decision rule:

A small p-value (typically ≤ 0.05) specifies solid proof against the null hypothesis (H₀), so you discard the null hypothesis.

A large p-value (> 0.05) specifies fragile proof against the null hypothesis, so you fail to discard the null hypothesis.

p-value = 0.20 > α = 0.05.

The null hypothesis was failed to rejected at 5% level of significance.

Thus, it can be concluded that there is not enough evidence to conclude that the mean score is less than 275 for young men nationwide.

Thus, the correct answer is option 2.