Researchers fed cockroaches a sugar solution. Ten hours later, they dissected the cockroaches and measured the amount of sugar in various tissues. Here are the amounts (in micrograms) of D-glucose in the hindguts of 5 cockroaches:
$$\begin{array} { l l l l l }
55.95 & 68.24 & 52.73 & 21.50 & 23.78
\end{array}$$ From previous work, the researchers expected the population of responses to be Normal. The insects are a random sample from a cockroach population grown in the laboratory. How should a 95% confidence interval for the mean amount of D-glucose in cockroach hindguts under these conditions be interpreted?

Question

Researchers fed cockroaches a sugar solution. Ten hours later, they dissected the cockroaches and measured the amount of sugar in various tissues. Here are the amounts (in micrograms) of D-glucose in the hindguts of 5 cockroaches:
$$\begin{array} { l l l l l } 
55.95 & 68.24 & 52.73 & 21.50 & 23.78
\end{array}$$ From previous work, the researchers expected the population of responses to be Normal. The insects are a random sample from a cockroach population grown in the laboratory. How should a 95% confidence interval for the mean amount of D-glucose in cockroach hindguts under these conditions be interpreted?

Quizplus · Accepted Answer

The confidence interval provides a range within which we are 95% confident that the true population mean of D-glucose in cockroach hindguts under these conditions falls. This does not mean that 95% of individual measurements will fall within this range, but rather that if we were to repeat the experiment many times, 95% of the calculated confidence intervals from those experiments would contain the true population mean.

Researchers Fed Cockroaches a Sugar Solution 55.9568.2452.7321.5023.78\begin{array} { l l l l l } 55.95 & 68.24 & 52.73 & 21.50 & 23.78\end{array}55.95​68.24​52.73​21.50​23.78​

Researchers Fed Cockroaches a Sugar Solution $\begin{array} { l l l l l } 55.95 & 68.24 & 52.73 & 21.50 & 23.78\end{array}$