An educator believes that new directed reading activities in the classroom will help elementary school pupils improve some aspects of their reading ability. She arranges for two third grade classes of students to take part in these activities. A third class of students in the same school is treated as control and does not take part in the reading activities. At the end of 8 weeks, all students are given a Degree of Reading Power (DRP) test, which measures the aspects of reading ability that the treatment is designed to improve. The educator wishes to see if the directed reading program changes scores on the DRP test. I calculated the appropriate 95% confidence interval using this data and found the interval to be 1.5 to 16.5. Does this indicate a true difference between the new reading activities and the control at the 5% level of significance?单项选择题
A
No, there is not a difference.
B
There is not enough information
C
Yes, there is a difference.

Question

An educator believes that new directed reading activities in the classroom will help elementary school pupils improve some aspects of their reading ability. She arranges for two third grade classes of students to take part in these activities. A third class of students in the same school is treated as control and does not take part in the reading activities. At the end of 8 weeks, all students are given a Degree of Reading Power (DRP) test, which measures the aspects of reading ability that the treatment is designed to improve. The educator wishes to see if the directed reading program changes scores on the DRP test. I calculated the appropriate 95% confidence interval using this data and found the interval to be 1.5 to 16.5. Does this indicate a true difference between the new reading activities and the control at the 5% level of significance?单项选择题

A

No, there is not a difference.

B

There is not enough information

C

Yes, there is a difference.

BlackTom AI · Accepted Answer

A 95% confidence interval that does not include 0 indicates a statistically significant difference at the 5% level.

1. Relevant knowledge points and concepts
- A confidence interval (CI) for a mean difference gives a range of plausible values for the population difference (treatment minus control).
- For a two-sided test at α = 0.05, the null hypothesis H0: difference = 0 is rejected if and only if the 95% CI does not contain 0.
- If the entire CI lies above 0, the treatment effect is positive; if entirely below 0, it is negative.

2. Step-by-step reasoning
- Null hypothesis: the directed reading activities produce no change in DRP scores (difference = 0).
- Given 95% CI for the difference = (1.5, 16.5).
- Check whether 0 is inside the interval. Since 0 < 1.5, 0 is not inside the interval.

3. Intermediate/calculation steps
- Lower bound = 1.5; upper bound = 16.5.
- Condition for significance: 0 ∉ (1.5, 16.5).
- Therefore, H0 is rejected at α = 0.05. (Equivalently, p-value < 0.05.)

4. Why the correct answer is correct
- Because the entire 95% CI lies above zero, the data provide statistically significant evidence (at the 5% level) that the reading activities increased DRP scores. The positive interval indicates a positive effect and excludes the null value of zero.

5. Why the other options are incorrect
- "No, there is not a difference." is incorrect because the CI excludes 0, so the null is rejected.
- "There is not enough information" is incorrect because the 95% CI alone contains the necessary information to conclude significance at the 5% level: whether 0 lies in the interval.