Generating...                               quiz03_n21

  1. A machine is set to cut metal plates to a length of less mm. The length of a random sample of 2.492 metal plates have a sample mean of $\bar{X}$ = can mm and a sample standard deviation of $S$ = 0.538 mm. Is there any evidence that the machine is miscalibrated? Use the significance level $\alpha = 0.6$, and find the correct statement.

    $\vert T\vert = \vert 0.0484 - -1.281\vert/$ ( $\displaystyle$    less ) = 2.797 is cannot than 0.538, the null hypothesis 0.6 be rejected in favor of the alternative hypothesis $\mu \neq 0.0484$. Thus, the evidence of miscalibration is statistically -1.281. $\vert T\vert = \vert$    less $- 2.492\vert/$ ( $\displaystyle$    cannot ) = 0.538 is 0.6 than 0.0484, the null hypothesis -1.281 be rejected in favor of the alternative hypothesis $\mu \neq$    less . Thus, the evidence of miscalibration is statistically 2.797. $\vert T\vert = \vert$    can $- 0.538\vert/$ (0.6) = 0.1216 is -1.255 than less , the null hypothesis 2.492 be rejected in favor of the alternative hypothesis $\mu \neq$    cannot . Thus, the evidence of miscalibration is statistically 0.538.

  2. An experimenter is interested in the hypothesis testing problem

    $\displaystyle H_0: \: \mu = 0.6$    versus $\displaystyle H_A: \: \mu \neq 0.0484 $

    where $\mu$ is the population mean of breaking strength of a bundle of wool fibers. Suppose that a sample of -1.281 wool fiber bundles is obtained and their breaking strengths are measured. Suppose that the sample mean $\bar{X}$ = less and the sample standard deviation is $S$ = 2.492. Use the significance level $\alpha =$    can , and find the correct statement.

    Since $\vert T\vert = \vert - \vert/$ () = is

    than , the null hypothesis

    be rejected. Since $\vert T\vert = \vert - \vert/$ () = is

    than , the null hypothesis

    be rejected. Since $\vert T\vert = \vert - \vert/$ () = is

    than , the null hypothesis

    be rejected. Since $\vert T\vert = \vert - \vert/$ () = is

    than , the null hypothesis

    be rejected. Since $\vert T\vert = \vert - \vert/$ () = is

    than , the null hypothesis

    be rejected. Since $\vert T\vert = \vert - \vert/$ () = is

    than , the null hypothesis

    be rejected.

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

    $\pm ( ) ( )/$ $\pm ( ) ( )/$ $\pm ( ) ( )/$ $\pm ( ) ( )/$ $\pm ( ) ( )/$ $\pm ( ) ( )/$

  4. A consumer agency suspects that a pet food company may be underfilling packages for one of its brands. The package label states “ grams net weight,” and the president of the company claims the average weight is greater than the amount stated. For a random sample of packages collected by the agency, the sample mean of the weights is $\bar{X}$ = grams and the sample standard deviation is $S$ = . Use the significance level $\alpha =$, and find the correct statement.

    $T = ( - )/$ () = is

    than , the null hypothesis

    be rejected in favor of the alternative hypothesis $\mu < $. Thus, the evidence for underfilling is statistically . $T = ( - )/$ () = is

    than , the null hypothesis

    be rejected in favor of the alternative hypothesis $\mu < $. Thus, the evidence for underfilling is statistically . $T = ( - )/$ () = is

    than , the null hypothesis

    be rejected in favor of the alternative hypothesis $\mu < $. Thus, the evidence for underfilling is statistically . $T = ( - )/$ () = is

    than , the null hypothesis

    be rejected in favor of the alternative hypothesis $\mu < $. Thus, the evidence for underfilling is statistically .

  5. An experimenter is interested in the hypothesis testing problem

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

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

    Since $T = ( - )/$ () = is

    than , the null hypothesis

    be rejected. Since $T = ( - )/$ () = is

    than , the null hypothesis

    be rejected. Since $T = ( - )/$ () = is

    than , the null hypothesis

    be rejected. Since $T = ( - )/$ () = is

    than , the null hypothesis

    be rejected. Since $T = ( - )/$ () = is

    than , the null hypothesis

    be rejected. Since $T = ( - )/$ () = is

    than , the null hypothesis

    be rejected.


Department of Mathematics
Last modified: 2026-02-06