Would the hypothesis that $\mu =5\mathrm{mg}$ be rejected at the $5\%$ level in favor of a two-sided alternative? Justify your answer.

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 $4.2\pm 2.3.$

Here,

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