Q.87 - The Practice of Statistics for AP

Question

Does this paper give convincing evidence that the mean amount of sugar in the hindguts under these conditions is not equal to $7 mg$? Justify your answer. 

Step-by-Step Solution

Answer

$7$does lie in the computed confidence interval.

Step 1: Given information

Given in the question that,  An understanding of cockroach biology may lead to an effective control strategy for these annoying insects. Researchers studying the absorption of sugar by insects feed a random sample of cockroaches a diet containing measured amounts of sugar. After$10$ hours, the cockroaches are killed and the concentration of the sugar in various body parts is determined by a chemical analysis. The paper that reports the research states that a $95\%$ confidence interval for the mean amount (in milligrams) of sugar in the hindguts of cockroaches is$4.2\pm 2.3.$

We need to find evidence for the mean amount of sugar in the hindguts under these conditions is not equal to $7 m.$

Step 2: Explanation

Given:

Confidence level $=95\%$

Confidence interval $=4.2\pm 2.3$

The confidence interval can be computed as:

$CI=4.2\pm 2.3$

    $=(1.9,6.5)$

Here, $7$does lie in the computed confidence interval.