9.1 Significance Tests - The Basics

When performing a significance test, we're looking for convincing evidence to __________ the null hypothesis in favor of the alternative hypothesis.

• refute

• dispute

• reject

• accept

To answer the question, "Is the evidence convincing enough to reject the null?" we can't just look at our sample statistic. Why not? Because samples ________.

• are all the same

• vary

• are too small

• affect the standard deviation

Tags

CCSS.HSS.IC.B.4

Small p-values mean that our sample was very unlikely if the null hypothesis is true. Therefore, small p-values are ________________ that the null hypothesis is wrong.

• convincing evidence

• believable proof

• reliable information

• justifiable inference

Tags

CCSS.HSS.ID.B.6B

The symbol for the significance level is ____.

Tags

CCSS.HSN.Q.A.1

Lumber companies dry freshly cut wood in kilns before selling it. A certain percentage of boards develop cracks on their ends during drying. The current drying procedure is known to produce cracks in 16% of boards. The drying supervisor wants to try a new method that she believes will result in a proportion of cracked boards that is less than 16%.

Write the appropriate hypotheses.

• Ho: p = 0.16

  Ha: p = 0.16

• Ho: p = 0.16

  Ha: p =/= 0.16

• Ho: p = 0.16

  Ha: p > 0.16

• Ho: p = 0.16

  Ha: p < 0.16

• Since our p-value of 0.027 is >undefined , we fail to reject the null hypothesis. We do not have convincing evidence that the new method is better. 

• Since our p-value of 0.0098 is less thanundefined, we fail to reject the null hypothesis. We have convincing evidence that the bottles contain less than 180 ml of liquid. 

• Since our p-value of 0.0098 is more thanundefined, we fail to reject the null hypothesis. We have convincing evidence that the bottles contain less than 180 ml of liquid. 

Resting pulse rate is an important measure of the fitness of a person's cardiovascular system, with a lower rate indicative of greater fitness. The mean pulse rate for all adult males is approximately 72 beats per minute. A random sample of 25 male students currently enrolled in the Agriculture School at a major university was selected and the mean resting pulse rate was found to be 80 beats per minute with a standard deviation of 20 beats per minute. The experimenter wishes to test if the students are less fit, on average, than the general population. The null and alternative hypotheses are:

• H₀: μ = 72; H_a: μ < 72

• H₀: x-bar = 72; H_a: x-bar < 72

• H₀: μ = 80; H_a: μ =72

• H₀: x-bar = 80; H_a: x-bar > 72

• H₀: μ = 72; H_a: μ > 72

Which of the following describes a Type II error in this setting?

• Concluding that the students are less fit (on average) than the general population when in fact they have equal fitness on average.

• Not concluding that the students are less fit (on average) as the general population when in fact they are less fit (on average).

• Not concluding that the students are less fit (on average) as the general population when in fact they have the same fitness (on average).

• Concluding that the students are less fit (on average) than the general population, when, in fact, they are less fit (on average).

• Concluding that the students have the same fitness (on average) when in fact they are more fit (on average).