Generating...                               quiz03_n27

  1. An experimenter is interested in the hypothesis testing problem

    $\displaystyle H_0: \: \mu = 400$    versus $\displaystyle H_A: \: \mu \neq 400 $

    where $\mu$ is the population mean of breaking strength of a bundle of wool fibers. Suppose that a sample of 22 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 $\alpha = 0.1$?

    The null hypothesis is rejected when $\vert T\vert > 1.323$ The null hypothesis is rejected when $\vert T\vert < 1.721$ The null hypothesis is rejected when $\vert T\vert < 1.717$ The null hypothesis is rejected when $\vert T\vert > 1.721$ The null hypothesis is rejected when $\vert T\vert > 1.717$ The null hypothesis is rejected when $\vert T\vert < 1.323$

  2. A machine is set to cut metal plates to a length of 80 mm. The length of a random sample of 19 metal plates have a sample mean of $\bar{X}$ = 79.989 mm and a sample standard deviation of $S$ = 0.161 mm. Is there any evidence that the machine is miscalibrated? Use the significance level $\alpha = 0.1$, and find the correct statement.

    $\vert T\vert = \vert 79.989 - 80\vert/$ ( $\displaystyle {{0.161}\over{\sqrt{19}}}$) = 0.298 is less than 1.33, the null hypothesis cannot be rejected in favor of the alternative hypothesis $\mu \neq 80$. Thus, the evidence of miscalibration is statistically not significant . $\vert T\vert = \vert 79.989 - 80\vert/$ ( $\displaystyle {{0.161}\over{\sqrt{19}}}$) = 0.298 is less than 1.734, the null hypothesis can be rejected in favor of the alternative hypothesis $\mu \neq 80$. Thus, the evidence of miscalibration is statistically significant . $\vert T\vert = \vert 79.989 - 80\vert/$ ( $\displaystyle {{0.161}\over{\sqrt{19}}}$) = 0.298 is less than 1.734, the null hypothesis cannot be rejected in favor of the alternative hypothesis $\mu \neq 80$. Thus, the evidence of miscalibration is statistically not significant .

  3. 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 $n$ = 21 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 $\alpha = 0.05$?

    The null hypothesis is rejected when $T > 2.086$ The null hypothesis is rejected when $T > 1.721$ The null hypothesis is rejected when $T > 1.725$ The null hypothesis is rejected when $T < 2.086$ The null hypothesis is rejected when $T < 1.725$ The null hypothesis is rejected when $T < 1.721$

  4. A sample of 10 observations has a sample mean $\bar{X} = 14.5$ and a sample standard deviation $S = 11.19$. Find a 99% two-sided confidence interval for the population mean.

    $14.5 \pm ( 3.25) ( 11.19)/$ $\displaystyle \sqrt{10}$ $14.5 \pm ( 3.169) ( 11.19)/$ $\displaystyle \sqrt{10}$ $14.5 \pm ( 3.25) ( 11.19)/$ 3 $14.5 \pm ( 2.821) ( 11.19)/$ $\displaystyle \sqrt{10}$ $14.5 \pm ( 2.764) ( 11.19)/$ $\displaystyle \sqrt{10}$ $14.5 \pm ( 2.821) ( 11.19)/$ 3

  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 $n$ = 15 bottles of the chemical solution is obtained and their densities are measured, and that the sample mean $\bar{X}$ = 0.824 and the sample standard deviation is $S$ = 0.149. Use the significance level $\alpha = 0.1$, and find the correct statement.

    Since $T = ( 0.824 - 0.6)/$ ( $\displaystyle {{0.149}\over{\sqrt{15}}}$) = 5.822 is greater than 1.345, the null hypothesis cannot be rejected. Since $T = ( 0.824 - 0.6)/$ ( $\displaystyle {{0.149}\over{\sqrt{15}}}$) = 5.822 is greater than 1.761, the null hypothesis can be rejected. Since $T = ( 0.824 - 0.6)/$ ( $\displaystyle {{0.149}\over{\sqrt{15}}}$) = 5.822 is greater than 1.761, the null hypothesis cannot be rejected. Since $T = ( 0.824 - 0.6)/$ ( $\displaystyle {{0.149}\over{\sqrt{14}}}$) = 5.625 is greater than 1.345, the null hypothesis can be rejected. Since $T = ( 0.824 - 0.6)/$ ( $\displaystyle {{0.149}\over{\sqrt{15}}}$) = 5.822 is greater than 1.345, the null hypothesis can be rejected. Since $T = ( 0.824 - 0.6)/$ ( $\displaystyle {{0.149}\over{\sqrt{14}}}$) = 5.625 is greater than 1.345, the null hypothesis cannot be rejected.


Department of Mathematics
Last modified: 2026-02-06