Question

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.

Answer 1

The 1st option is correct:

the current study does provide significant evidence that the mean score is different between the two populations, since 74 falls outside the confidence interval.

Explanation:

Since 74 falls out of the interval, we go with the 1st option,

the current study does provide significant evidence that the mean score is different between the two populations, since 74 falls outside the confidence interval.