9. Hypothesis Testing for One Sample

Mark ‘TRUE’ or ‘FALSE’ for each of the following.

$\left(A\right)$ The test statistic & the critical value are the same thing.

Mark ‘TRUE’ or ‘FALSE’ for each of the following.

$\left(B\right)$ The critical value is the boundary of the rejection region.

Mark ‘TRUE’ or ‘FALSE’ for each of the following.

$\left(C\right)$ You should always reject $H_0$ if the test statistic is greater than the critical value.

Use α to find the critical value(s), then determine if the given test statistic is in the rejection region.

$\left(A\right)$ $H_0:\mu =7.5$; $H_a:\mu >7.5$

$\alpha =0.01;z=2.17$

Test is [ LEFT | TWO | RIGHT ] -tailed

Critical Value(s):

Test stat [ IN | NOT IN ] rejection region.

Use α to find the critical value(s), then determine if the given test statistic is in the rejection region.

$\left(B\right)$ $H_0:p=0.64$;

$\alpha =0.10;z=-1.53$

Test is [ LEFT | TWO | RIGHT ] -tailed

Critical Value(s):

Test stat [ IN | NOT IN ] rejection region.

Use α to find the critical value(s), then determine if the given test statistic is in the rejection region.

$\left(C\right)$ $H_0:\mu =98.6$; $H_a:\mu \ne 98.6$

$\alpha =0.05$

$t=2.41;df=17$

Test is [ LEFT | TWO | RIGHT ] -tailed

Critical Value(s):

Test stat [ IN | NOT IN ] rejection region.

Use α to find the critical value(s), then determine if the given test statistic is in the rejection region.

$\left(D\right)$ $H_0:{\sigma }^2=0.3;H_a:{\sigma }^2>0.3$

$\alpha =0.05$

${\chi }^2=61.7;df=51$

Test is [ LEFT | TWO | RIGHT ] -tailed

Critical Value(s):

Test stat [ IN | NOT IN ] rejection region.

A soup company claims that the average sodium content of their most popular soup is 500 mg per can. A nutritionist collects a sample of 36 cans with mean sodium content 507 mg. Assume a known pop. standard deviation of 15 mg & test the nutritionist’s suspicion that the mean sodium content is more than 500 mg using the critical value method with $\alpha =0.01$

$H_0:\mu =$ ____ $H_a:\mu$ ______

$\bar{x}=$ ______ $\sigma =$ ______ $n=$ ______

$z=$

Critical Value(s):

Because test stat. $\left(z\right)$ is [ INSIDE | OUTSIDE ] rejection region, we [ REJECT | FAIL TO REJECT ] $H_0$. There is [ ENOUGH | NOT ENOUGH ] evidence to conclude that…