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.

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 ________.

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.

The symbol for the significance level is ____.

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.

The drying supervisor uses the new method on a random sample of 200 boards.  She conducts a hypothesis test on her sample data and gets a p-value of .027. Based on the p-value , was there convincing evidence that the new method is better? Use  $$\alpha$$  = 0.05.

The label on bottles of one company's grapefruit juice say that they contain 180 ml of liquid. Your friend Jerry suspects that the true mean is less than that, so he takes a random sample of 40 bottles and measures the volume of liquid in each bottle. The mean volume of liquid in the bottles is 179.5 ml and the standard deviation is 1.3 ml. Jerry performs a test of Ho: $$\mu$$ = 180 ml versus Ha:< 180 ml. The test yields a p-value of 0.0098.  

Using a significance level of 1%, is there convincing evidence that there is less than 180 ml of liquid in the bottles? 

Simon reads a newspaper report claiming that 12% of all adults in the US are left-handed. He wonders if this figure holds true at his college. Simon chooses an SRS of 100 students and 16 of them are left-handed. He performs a test of Ho: p = 0.12 versus Ha: =/= 0.12. 

The test yields a p-value of 0.2184. What conclusion would you make for a significance level of $$\alpha$$ = 0.10?

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:

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