Homeschooling can be beneficial and certain groups may benefit more than others.
Suppose a random sample of 100 homeschooled children from a black community took an academic achievement test and scored, on average 89 points out of 100.
The population standard deviation on this measure is known to be 9.8.
A previous study showed that the public school students from the same community score an average of 74 points on this test.
We would like to test (at the usual significance level of 5%) whether the current study provides significant evidence that this mean is different between groups.
Using a 95% confidence interval of (83, 92), our conclusion is that:
the current study does provide significant evidence that the mean score is different between the two populations, since 74 falls outside the confidence interval.
the current study does provide significant evidence that the mean score is different between the two populations, since 74 does not fall outside the confidence interval.
the current study does not provide significant evidence that the mean score is different between the two populations, since 74 falls outside the confidence interval.
the current study does not provide significant evidence that the mean score is different between the two populations, since 74 falls inside the confidence interval.
None of the above. The only way to reach a conclusion is by finding the p-value of the test.
The correct answer is: the current study does provide significant evidence that the mean score is different between the two populations, since 74 falls outside the confidence interval.
The correct answer is:
None of the above. The only way to reach a conclusion is by finding the p-value of the test.
To determine whether the current study provides significant evidence that the mean score is different between the two populations, we need to perform a hypothesis test. The confidence interval alone cannot lead to a conclusion about significance.
In this case, we can set up the following hypotheses:
H0: μ1 - μ2 = 0 (There is no difference in mean scores between homeschooled children and public school students from the same community).
Ha: μ1 - μ2 ≠ 0 (There is a difference in mean scores between the two populations).
We can then perform a two-sample t-test to determine the p-value. Based on that, we can assess whether there is significant evidence to support rejecting the null hypothesis.
Therefore, none of the provided options can be concluded solely from the confidence interval.