91Ó°ÊÓ

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 $4.2Â\pm 2.3.$

Here,

Confidence level =$95\%$

Confidence interval $=4.2Â\pm 2.3$

The confidence interval can be computed as:

$CI=4.2Â\pm 2.3$

$=(1.9,6.5)$

Here, $5$ lies in the computed confidence interval. In this way, the null hypothesis that expresses that $\mathrm{μ}=5mg$wouldn't be rejected at $5\%$ significance level..