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 -4.5 to 8.5. 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
There is not enough information
B
Yes, there is a difference.
C
No, there is not 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 -4.5 to 8.5. 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

There is not enough information

B

Yes, there is a difference.

C

No, there is not a difference.

BlackTom AI · Accepted Answer

A 95% confidence interval that includes 0 implies there is no statistically significant difference at the 5% level.

1. Relevant concepts
- Null hypothesis H0: the true mean difference (treatment − control) = 0. Alternative H1: difference ≠ 0.
- A 95% confidence interval (CI) for the mean difference gives the range of values that are plausible for the true difference with 95% confidence.
- If the CI contains 0, the data are consistent with no effect; equivalently, a two-tailed hypothesis test at α = 0.05 would fail to reject H0.

2. Step-by-step reasoning
- The calculated 95% CI for the difference is −4.5 to 8.5.
- Check whether 0 is inside this interval. Since −4.5 ≤ 0 ≤ 8.5, 0 lies inside the interval.
- Because the CI includes 0, the observed difference is not statistically distinguishable from zero at the 5% significance level.

3. Calculations / intermediate steps
- No raw sample statistics are provided here, but the critical logical calculation is the membership test: is 0 between −4.5 and 8.5? Yes.
- Relation: CI excludes 0 ⇔ two-tailed p-value < 0.05. Here CI includes 0 ⇔ p-value ≥ 0.05.

4. Why the correct answer is correct
- The CI including zero indicates the true difference could be zero; therefore there is insufficient evidence to conclude a true effect of the reading activities at the 5% level.

5. Why other options are incorrect
- “Yes, there is a difference.” Incorrect because that requires the 95% CI to exclude 0 (e.g., entirely positive or entirely negative), which is not the case.
- “There is not enough information.” Incorrect because the provided 95% CI directly answers the question about significance at the 5% level.