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 m1? What is the P-value for the appropriate null and alternative hypotheses?

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 m1? What is the P-value for the appropriate null and alternative hypotheses?

Quizplus · Accepted Answer

To determine if the true population mean solution volume is not 1 ml, we perform a two-tailed hypothesis test. The null hypothesis is that the true mean is 1 ml (μ = 1), and the alternative hypothesis is that the true mean is not 1 ml (μ ≠ 1). We calculate the sample mean and use the given standard deviation (σ = 0.05 ml) along with the sample size (n = 8) to find the test statistic. Then, we find the p-value associated with this test statistic under the normal distribution. The p-value of 0.322 suggests that there is not enough evidence to reject the null hypothesis at common significance levels (e.g., 0.05), indicating that the data do not provide strong evidence that the true population mean solution volume is different from 1 ml.

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A Company Manufactures U-100 Insulin Syringes Designed to Contain 1 $\begin{array} { | l | l | l | l | l | l | l | l | } \hline 1.05 & 1.04 & 1.06 & 1.01 & 0.98 & 0.98 & 1.03 & 0.99 \\\hline\end{array}$