QUIZ: Hypothesis Z- and T-Test

When should you use the t-test? (select all that apply)

• When you are testing a proportion/percentage of a population

• When you are testing for a mean

• When you are given the population standard deviation

• When you are ONLY given the sample standard deviation

Tags

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

Hypotheses must have a parameter or statistic such as  $\overline{x},\ \mu,\ \sigma,\ s$  

• True

• False

Tags

CCSS.HSS.IC.A.1

You do not need BOTH null and alternate hypotheses when testing

• True

• False

When testing with  $\alpha=0.01$  you get  $p=0.12$ . Your decision should be 

• Reject $H_0$ , there is a significant difference

• Accept $H_0$ , there is NOT a significant difference

• Reject $H_0$ , there is NOT a significant difference

• Accept $H_0$ , there is a significant difference

Tags

CCSS.HSS.IC.B.5

CCSS.HSS.MD.B.7

When testing with  $\alpha=0.05$  you get  $p=3.2\ E^{-6}$ . Your decision should be 

• Reject $H_0$ , there is a significant difference

• Accept $H_0$ , there is NOT a significant difference

• Reject $H_0$ , there is NOT a significant difference

• Accept $H_0$ , there is a significant difference

Tags

CCSS.HSS.IC.B.5

For the t-test one uses __________ instead of σ.

• n

• s

• χ²

• t

If you wish to test the claim that the mean of the population is 100, the appropriate alternate hypothesis is

•  $\overline{x}=100$  

•  $\mu=100$  

•  $\mu\ne100$  

•  $\mu>100$  

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.ID.A.4

A U.S. Web Usage Snapshot indicated a monthly average of 36 Internet visits per user from home. A random sample of 24 Internet users yielded a sample mean of 42.1 visits with a standard deviation of 5.3. With $\alpha=0.01$ can it be concluded that this differs from the national average? List test, p-value, and decision.

• z-test,  $p=1.72E^{-8}$ , Reject  $H_0$  

• z-test,  $p=1.72E^{-8}$ , Accept $H_0$  

• t-test,  $p=4.86E^{-6}$  , Reject $H_0$  

• t-test,  $p=9.71E^{-6}$  , Reject $H_0$ 

A real estate agent believes that the average closing cost of purchasing a new home is $6500. She selects 40 new home sales at random and finds that the average closing costs are $6600. The standard deviation of the population is $120. Test her belief at $\alpha=0.05$ . List test, p-value, and decision.

• z-test,  $p=1.36E^{-7}$ , Reject  $H_0$  

• z-test,  $p=6.81E^{-8}$ , Accept $H_0$  

• t-test,  $p=5.32E^{-6}$  , Reject $H_0$  

• t-test,  $p=2.66E^{-6}$  , Accept $H_0$ 

In a New York modeling agency, a researcher wishes to see if the average height of female models is really less than 67 inches, as the chief claims. A random sample of 20 models has an average height of 65.8 inches. The standard deviation of the sample is 1.7 inches. At $\alpha=0.05$ , is the average height of the models really less than 67 inches? List test, p-value, and decision.

• z-test,  $p=0.002$ , Accept $H_0$ 

• z-test,  $p=7.98E^{-4}$ , Reject $H_0$ 

• t-test,  $p=0.003$ , Reject $H_0$ 

• t-test,  $p=0.005$ , Reject $H_0$