The state government claims that the average earnings for a high school student who works during the summer is $1,500. A survey of 200 local high school students determined that the average amount of money earned at a summer job in the area was $1,100 and a 90% confidence interval was found to be ($975, $1,225). The confidence level is interpreted to mean that:
Answer
A
if the study were to be repeated many times, there is a 90% probability that the true amount earned at a summer job is $1,500.
B
if we repeat our survey many times, then about 90% of our confidence intervals will contain the true amount earned at a summer job.
C
because our 90% confidence interval does not contain $1,500 there is a 90% probability the true amount earned at a summer job is not $1,500.
D
if we were to repeat our survey many times, then about 90% of all the confidence intervals will contain the value $1,500.
Explanation
A 90% confidence level describes how the interval-making method performs over many repeated surveys: about 90% of the resulting intervals would contain the true average earnings. It does not mean there is a 90% probability that a fixed value such as $1,500 is correct or incorrect. Therefore, the correct choice is B.
AI-written and checked against the verified answer.