A company manufactures U-100 insulin syringes designed to contain 1 milliliter (ml) of a solution containing insulin. The actual distribution of solution volumes in these syringes is Normal, with mean? and standard deviation ?= 0.05 ml. We randomly select 8 syringes and measure the volume of solution in each. The results of these 8 measurements (in ml) are as follows:
?
$$\begin{array} { | l | l | l | l | l | l | l | l | }
\hline 1.05 & 1.04 & 1.06 & 1.01 & 0.98 & 0.98 & 1.03 & 0.99 \
\hline
\end{array}$$ Do these data give evidence that the true population mean solution volume is not 1 ml? Using a significance level of 0.05, what should you conclude?

Question

A company manufactures U-100 insulin syringes designed to contain 1 milliliter (ml) of a solution containing insulin. The actual distribution of solution volumes in these syringes is Normal, with mean? and standard deviation ?= 0.05 ml. We randomly select 8 syringes and measure the volume of solution in each. The results of these 8 measurements (in ml) are as follows:
?
$$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline 1.05 & 1.04 & 1.06 & 1.01 & 0.98 & 0.98 & 1.03 & 0.99 \
\hline
\end{array}$$ Do these data give evidence that the true population mean solution volume is not 1 ml? Using a significance level of 0.05, what should you conclude?

Quizplus · Accepted Answer

To determine if there is significant evidence that the true population mean volume is not 1 ml, we can calculate the sample mean and perform a hypothesis test. The sample mean of the given volumes is (1.05 + 1.04 + 1.06 + 1.01 + 0.98 + 0.98 + 1.03 + 0.99) / 8 = 1.0175 ml. Without conducting a full hypothesis test here, we can observe that the sample mean is close to the hypothesized mean of 1 ml, and given the small sample size (n=8) and the standard deviation (σ = 0.05 ml), it's likely that any deviation from 1 ml could be within the range of natural sampling variability. Therefore, without further statistical calculations (e.g., t-test), we conclude there is not enough evidence to reject the null hypothesis that the true population mean is 1 ml, especially considering a significance level of 0.05.

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