This question is incomplete, the complete question is;
Question 1: The National Assessment of Educational Progress (NAEP) is administered annually to 4th, 8th, and 12th graders in the United States. On the math assessment, a score above 275 is considered an indication that a student has the skills to balance a checkbook. In a random sample of 500 young men between the ages of 18 and 20, the mean NAEP math score is 272 with standard deviation of 78.
Do we have evidence to support the claim that young men nationwide have a mean score below 275. The level of significance is 5%
Answer:
p-value ( 0.2 ) > significance level (0.05 )
Fail to reject H₀ at ∝ = 0.05
Therefore, We do not have enough evidence to conclude that the mean score is less than 275 for young men nationwide.
Step-by-step explanation:
Given the data in the question;
Null hypothesis H₀ : μ = 275
Alternative hypothesis Hₐ : μ < 275
mean x' = 272
standard deviation σ = 78
sample size n = 500
Test Statistics
z = (x'-μ) / (σ /√n )
we substitute
z = (272-275) / (78 /√500 )
z = -3 / 3.488266
z = - 0.86
from table;
p-value = 0.19489 ≈ 0.2
Hence; p-value ( 0.2 ) > significance level (0.05 )
Fail to reject H₀ at ∝ = 0.05
Therefore, We do not have enough evidence to conclude that the mean score is less than 275 for young men nationwide.