A score of 243 is a "basic" reading level.
Scores for a random sample of 3000 students had a xbar = 250 with a standard error 1.0
The 99% confidence interval for the mean score all students in the city is 247.4 to 252.6.
Ques: Is there good evidence that the mean for all students in the city is less than the basic level?
Ans: 243 is not in the 99% confidence level. It is below.
The answer in the back of the book says:"we would fail to reject Ho: u=243 against the one-sided alternative hypothesis Ha: u (less than) 243 at the 1% significance level."
I do not understand the book answer "we would fail to reject..."
Does this mean there IS good evidence that the mean is less than the basic level? or NOT?
Ho: µ = 243
Ha: µ < 243
I would definitely reject Ha. But since we have only two hypotheses, that would leave me to "fail to reject" Ho. However, I would rather accept Ha: µ > 243, but that was not an included hypothesis.
The statement "we would fail to reject the null hypothesis Ho: u=243 against the one-sided alternative hypothesis Ha: u < 243 at the 1% significance level" means that there is not enough evidence to conclude that the mean is less than the basic level.
In hypothesis testing, we start with a null hypothesis (Ho) and an alternative hypothesis (Ha). The null hypothesis is the statement that we assume to be true initially, while the alternative hypothesis is the statement we are trying to gather evidence for.
In this case, the null hypothesis is that the mean score for all students in the city is equal to 243 (Ho: u=243), while the alternative hypothesis is that the mean score is less than 243 (Ha: u < 243).
To determine whether there is evidence to support the alternative hypothesis, we conduct a hypothesis test. One way to do this is by constructing a confidence interval and examining whether the value of interest (243 in this case) falls within that interval.
In this scenario, the 99% confidence interval for the mean score of all students in the city is 247.4 to 252.6. Since the value of interest (243) is below this interval, it means that there is not enough evidence to conclude that the mean score is less than the basic level.
Therefore, based on the given information, we do not have good evidence to support the claim that the mean for all students in the city is less than the basic level.