Generating...                               quiz03_n9

  1. A machine is set to cut metal plates to a length of 80 mm. The length of a random sample of 14 metal plates have a sample mean of $\bar{X}$ = 80.009 mm and a sample standard deviation of $S$ = 0.085 mm. Is there any evidence that the machine is miscalibrated? Use the significance level $\alpha = 0.05$, and find the correct statement.

    $\vert T\vert = \vert 80.009 - 80\vert/$ ( $\displaystyle {{0.085}\over{\sqrt{14}}}$) = 0.396 is less than 2.16, the null hypothesis can be rejected in favor of the alternative hypothesis $\mu \neq 80$. Thus, the evidence of miscalibration is statistically significant . $\vert T\vert = \vert 80.009 - 80\vert/$ ( $\displaystyle {{0.085}\over{\sqrt{14}}}$) = 0.396 is less than 2.16, the null hypothesis cannot be rejected in favor of the alternative hypothesis $\mu \neq 80$. Thus, the evidence of miscalibration is statistically not significant . $\vert T\vert = \vert 80.009 - 80\vert/$ ( $\displaystyle {{0.085}\over{\sqrt{14}}}$) = 0.396 is less than 1.771, the null hypothesis cannot be rejected in favor of the alternative hypothesis $\mu \neq 80$. Thus, the evidence of miscalibration is statistically not significant .

  2. An experimenter is interested in the hypothesis testing problem

    $\displaystyle H_0: \: \mu = 200$    versus $\displaystyle H_A: \: \mu \neq 200 $

    where $\mu$ is the population mean of breaking strength of a bundle of wool fibers. Suppose that a sample of 23 wool fiber bundles is obtained and their breaking strengths are measured. For what values of the $t$-statistic $T$ does the experimenter reject the null hypothesis with significance level $\alpha = 0.01$?

    The null hypothesis is rejected when $\vert T\vert < 2.819$ The null hypothesis is rejected when $\vert T\vert < 2.807$ The null hypothesis is rejected when $\vert T\vert < 2.508$ The null hypothesis is rejected when $\vert T\vert > 2.819$ The null hypothesis is rejected when $\vert T\vert > 2.508$ The null hypothesis is rejected when $\vert T\vert > 2.807$

  3. An experimenter is interested in the hypothesis testing problem

    $\displaystyle H_0: \: \mu = 300$    versus $\displaystyle H_A: \: \mu \neq 300 $

    where $\mu$ is the population mean of breaking strength of a bundle of wool fibers. Suppose that a sample of 25 wool fiber bundles is obtained and their breaking strengths are measured. Suppose that the sample mean $\bar{X}$ = 266.72 and the sample standard deviation is $S$ = 54.6. Use the significance level $\alpha = 0.01$, and find the correct statement.

    Since $\vert T\vert = \vert 266.72 - 300\vert/$ ( $\displaystyle {{27.3}\over{\sqrt{6}}}$) = 2.986 is greater than 2.797, the null hypothesis can be rejected. Since $\vert T\vert = \vert 266.72 - 300\vert/$ (10.92) = 3.048 is greater than 2.492, the null hypothesis cannot be rejected. Since $\vert T\vert = \vert 266.72 - 300\vert/$ (10.92) = 3.048 is greater than 2.797, the null hypothesis can be rejected. Since $\vert T\vert = \vert 266.72 - 300\vert/$ (10.92) = 3.048 is greater than 2.492, the null hypothesis can be rejected. Since $\vert T\vert = \vert 266.72 - 300\vert/$ (10.92) = 3.048 is greater than 2.797, the null hypothesis cannot be rejected. Since $\vert T\vert = \vert 266.72 - 300\vert/$ ( $\displaystyle {{27.3}\over{\sqrt{6}}}$) = 2.986 is greater than 2.797, the null hypothesis cannot be rejected.

  4. An experimenter is interested in the hypothesis testing problem

    $\displaystyle H_0: \: \mu = 0.9$    versus $\displaystyle H_A: \: \mu > 0.9 $

    where $\mu$ is the population mean of the density of a chemical solution. Suppose that a sample of $n$ = 17 bottles of the chemical solution is obtained and their densities are measured. For what values of the $t$-statistic $T$ does the experimenter reject the null hypothesis with significance level $\alpha = 0.1$?

    The null hypothesis is rejected when $T > 1.337$ The null hypothesis is rejected when $T > 1.333$ The null hypothesis is rejected when $T < 1.337$ The null hypothesis is rejected when $T < 1.333$ The null hypothesis is rejected when $T > 1.746$ The null hypothesis is rejected when $T < 1.746$

  5. An experimenter is interested in the hypothesis testing problem

    $\displaystyle H_0: \: \mu = 0.6$    versus $\displaystyle H_A: \: \mu > 0.6 $

    where $\mu$ is the population mean of the density of a chemical solution. Suppose that a sample of $n$ = 14 bottles of the chemical solution is obtained and their densities are measured, and that the sample mean $\bar{X}$ = 0.791 and the sample standard deviation is $S$ = 0.448. Use the significance level $\alpha = 0.05$, and find the correct statement.

    Since $T = ( 0.791 - 0.6)/$ ( $\displaystyle {{0.448}\over{\sqrt{14}}}$) = 1.595 is less than 2.16, the null hypothesis can be rejected. Since $T = ( 0.791 - 0.6)/$ ( $\displaystyle {{0.448}\over{\sqrt{13}}}$) = 1.537 is less than 1.771, the null hypothesis can be rejected. Since $T = ( 0.791 - 0.6)/$ ( $\displaystyle {{0.448}\over{\sqrt{14}}}$) = 1.595 is less than 2.16, the null hypothesis cannot be rejected. Since $T = ( 0.791 - 0.6)/$ ( $\displaystyle {{0.448}\over{\sqrt{13}}}$) = 1.537 is less than 1.771, the null hypothesis cannot be rejected. Since $T = ( 0.791 - 0.6)/$ ( $\displaystyle {{0.448}\over{\sqrt{14}}}$) = 1.595 is less than 1.771, the null hypothesis cannot be rejected. Since $T = ( 0.791 - 0.6)/$ ( $\displaystyle {{0.448}\over{\sqrt{14}}}$) = 1.595 is less than 1.771, the null hypothesis can be rejected.


Department of Mathematics
Last modified: 2026-07-16