A manufacturer's process for analyzing aspirin tablets has a known variance of 25. A sample of ten aspirin tablets is selected and analyzed for the amount of aspirin, yielding the following results [latex] \begin{array}{llllllllll} 254 & 249 & 252 & 252 & 249 & 249 & 250 & 247 & 251 & 252 \end{array} [/latex] Determine whether there is any evidence that the measurement process is not under statistical control at [latex]\alpha=0.05[/latex].

The variance for the sample of ten tablets is 4.3. A two-tailed significance test is used since the measurement process is considered out of statistical control if the sample's variance is either too good or too poor. The null hypothesis and alternative hypotheses are [latex]H_{0}: \quad s^{2}=\sigma^{2} \quad H_{\mathrm{A}}: \quad s^{2} \neq \sigma^{2}[/latex] The test statistic is [latex]F_{\text {exp }}=\frac{\sigma^{2}}{s^{2}}=\frac{25}{4.3}=5.8[/latex] The critical value for [latex]F(0.05, \infty, 9)[/latex] from Appendix [latex]1 C[/latex] is 3.33. Since [latex]F[/latex] is greater than [latex]F(0.05, \infty, 9)[/latex], we reject the null hypothesis and accept the alternative hypothesis that the analysis is not under statistical control. One explanation for the unreasonably small variance could be that the aspirin tablets were not selected randomly.

Question 4.17: A manufacturer’s process for analyzing aspirin tablets has a...

Modern Analytical Chemistry

A manufacturer’s process for analyzing aspirin tablets has a known variance of 25. A sample of ten aspirin tablets is selected and analyzed for the amount of aspirin, yielding the following results

$\begin{array}{llllllllll} 254 & 249 & 252 & 252 & 249 & 249 & 250 & 247 & 251 & 252 \end{array}$

Determine whether there is any evidence that the measurement process is not under statistical control at $\alpha=0.05$ .

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The variance for the sample of ten tablets is 4.3. A two-tailed significance test is used since the measurement process is considered out of statistical control if the sample’s variance is either too good or too poor. The null hypothesis and alternative hypotheses are

$H_{0}: \quad s^{2}=\sigma^{2} \quad H_{\mathrm{A}}: \quad s^{2} \neq \sigma^{2}$

The test statistic is

$F_{\text {exp }}=\frac{\sigma^{2}}{s^{2}}=\frac{25}{4.3}=5.8$

The critical value for $F(0.05, \infty, 9)$ from Appendix $1 C$ is 3.33. Since $F$ is greater than $F(0.05, \infty, 9)$ , we reject the null hypothesis and accept the alternative hypothesis that the analysis is not under statistical control. One explanation for the unreasonably small variance could be that the aspirin tablets were not selected randomly.