Question

9. A recent study examining the effects of sugar consumption on a middle

school student's ability to focus on a reading assignment used 18 volunteer
subjects and divided them into 9 pairs based on their reading speeds. One
randomly assigned member of each pair was given a beverage containing a
substantial amount of sugar, and the other drank a sugar-free version of the
beverage. Each subject was given a passage to read and the time (in seconds) it
took to read was recorded.
The difference for each pair is calculated sugar - sugar-free). A 90% confidence
interval for the mean difference in reading times is (-5.8, 0.15).
(A) Because the center of the interval is -2.825, we have convincing evidence that sugar
causes faster reading times, on average.
(B) Because the confidence interval includes 0, we don't have convincing evidence that
sugar causes faster reading times, on average.
(C) Because the confidence interval includes 0, we have convincing evidence that sugar
causes faster reading times, on average.
(D) Because the confidence interval includes more negative than positive values, we
have convincing evidence that sugar causes faster reading times, on average.
Se
(E) Causation should not be inferred because the subjects were volunteers.​

Answer 1

(B) Because the confidence interval includes 0, we don't have convincing evidence that sugar causes faster reading times, on average.

Explanation:

Confidence Interval for the population mean difference in reading is basically an interval of range of values where the true population mean difference in reading time can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

In using confidence interval of population mean difference in reading times for hypothesis testing, if the interval obtained contains a value of 0, it means the population mean difference in reading times can take on a value of 0 and indicate that there isn't enough evidence to conclude that there is a significant difference in the two quantities being compared. (The null hypothesis is true).

If the interval doesn't contain a 0, then it can be concluded that there is enough evidence to conclude that there is significant difference in the two quantities being compared.

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