Generating...                               quiz07c_n5

  1. 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 $n$ = 16 bottles of the chemical solution is obtained and their densities are measured, and that the sample mean $\bar{X}$ = 0.825 and the sample standard deviation is $S$ = 0.466. Use the significance level $\alpha = 0.01$, and find the correct statement.

    Since $T = ( 0.825 - 0.6)/$ (0.1165) = 1.931 is less than 2.602, the null hypothesis cannot be rejected. Since $T = ( 0.825 - 0.6)/$ (0.1165) = 1.931 is less than 2.947, the null hypothesis can be rejected. Since $T = ( 0.825 - 0.6)/$ (0.1165) = 1.931 is less than 2.947, the null hypothesis cannot be rejected. Since $T = ( 0.825 - 0.6)/$ ( $\displaystyle {{0.466}\over{\sqrt{15}}}$) = 1.87 is less than 2.602, the null hypothesis cannot be rejected. Since $T = ( 0.825 - 0.6)/$ ( $\displaystyle {{0.466}\over{\sqrt{15}}}$) = 1.87 is less than 2.602, the null hypothesis can be rejected. Since $T = ( 0.825 - 0.6)/$ (0.1165) = 1.931 is less than 2.602, the null hypothesis can be rejected.

  2. A sample of 13 observations has a sample mean $\bar{X} = 24.69$ and a sample standard deviation $S = 14.0$. Find a 99% two-sided confidence interval for the population mean.

    $24.69 \pm ( 3.012) ( 14.0)/$ $\displaystyle \sqrt{13}$ $24.69 \pm ( 2.65) ( 14.0)/$ $\displaystyle \sqrt{13}$ $24.69 \pm ( 2.681) ( 14.0)/$ $\displaystyle 2\,\sqrt{3}$ $24.69 \pm ( 3.055) ( 14.0)/$ $\displaystyle 2\,\sqrt{3}$ $24.69 \pm ( 3.055) ( 14.0)/$ $\displaystyle \sqrt{13}$ $24.69 \pm ( 2.681) ( 14.0)/$ $\displaystyle \sqrt{13}$

  3. A consumer agency suspects that a pet food company may be underfilling packages for one of its brands. The package label states “ 1200 grams net weight,” and the president of the company claims the average weight is greater than the amount stated. For a random sample of 14 packages collected by the agency, the sample mean of the weights is $\bar{X}$ = 1154.706 grams and the sample standard deviation is $S$ = 29.391. Use the significance level $\alpha = 0.1$, and find the correct statement.

    $T = ( 1154.706 - 1200)/$ ( $\displaystyle {{29.391}\over{\sqrt{13}}}$) = -5.556 is less than -1.35, the null hypothesis can be rejected in favor of the alternative hypothesis $\mu < 1200$. Thus, the evidence for underfilling is statistically significant . $T = ( 1154.706 - 1200)/$ ( $\displaystyle {{29.391}\over{\sqrt{14}}}$) = -5.766 is less than -1.35, the null hypothesis cannot be rejected in favor of the alternative hypothesis $\mu < 1200$. Thus, the evidence for underfilling is statistically not significant . $T = ( 1154.706 - 1200)/$ ( $\displaystyle {{29.391}\over{\sqrt{14}}}$) = -5.766 is less than -1.35, the null hypothesis can be rejected in favor of the alternative hypothesis $\mu < 1200$. Thus, the evidence for underfilling is statistically significant . $T = ( 1154.706 - 1200)/$ ( $\displaystyle {{29.391}\over{\sqrt{13}}}$) = -5.556 is less than -1.35, the null hypothesis cannot be rejected in favor of the alternative hypothesis $\mu < 1200$. Thus, the evidence for underfilling is statistically not significant .

  4. 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 14 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 $\vert T\vert < 1.35$ The null hypothesis is rejected when $\vert T\vert < 1.761$ The null hypothesis is rejected when $\vert T\vert > 1.35$ The null hypothesis is rejected when $\vert T\vert > 1.761$ The null hypothesis is rejected when $\vert T\vert > 1.771$ The null hypothesis is rejected when $\vert T\vert < 1.771$

  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 $n$ = 26 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 $\alpha = 0.01$?

    The null hypothesis is rejected when $T < 2.485$ The null hypothesis is rejected when $T < 2.479$ The null hypothesis is rejected when $T < 2.787$ The null hypothesis is rejected when $T > 2.787$ The null hypothesis is rejected when $T > 2.479$ The null hypothesis is rejected when $T > 2.485$


Department of Mathematics
Last modified: 2025-05-04