Hypothesis Tests

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

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.IC.A.1

CCSS.HSS.IC.B.5

CCSS.HSS.ID.A.4

The symbol for the significance level is ____.

• $\alpha$

• $\theta$

• $\pi$

• $\mu$

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

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.

• Since our p-value of 0.027 is < $\alpha$  , we reject the null hypothesis. We have convincing evidence that the new method is better. 

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

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.5

CCSS.HSS.IC.B.3

Last year, a pineapple company in Hawaii grew pineapples that weighed an average of 31 ounces. The company installed a new irrigation system hoping that this year’s crop of pineapples would be larger than 31 ounces.

Write appropriate hypotheses.

• Ho: u = 31 ounces

  Ha: u > 31 ounces

• Ho: u = 31 ounces

  Ha: u < 31 ounces

• Ho: u = 31 ounces

  Ha: u =/= 31 ounces

• Ho: u = 31 ounces

  Ha: u = 31 ounces

At the end of the current growing season, the quality inspector took a sample of 50 pineapples and conducted a hypothesis test on the sample data. His test produced a p-value of 0.1317. Based on the p-value, was there convincing evidence that the current pineapples are larger? Use  $\alpha$  =0.05. 

• Since our p-value of 0.1317 is < $\alpha$  , we reject the null hypothesis. We have convincing evidence that the pineapples are larger. 

• Since our p-value of 0.1317 is > $\alpha$  , we fail to reject the null hypothesis. We do not have convincing evidence that the pineapples are larger. 

Suppose the P-value for a hypothesis test is 0.0304. Using a = 0.05, what is the appropriate conclusion?

• a) Reject the null hypothesis

• b) Reject the alternative hypothesis

• c) Fail to reject the null hypothesis

• d) Fail to reject the alternative hypothesis

At the Chrysler manufacturing plant, there is a part that is supposed to weigh precisely 19 pounds. The engineers take a sample of parts and want to know if they meet the weight specifications. What are our null and alternative hypotheses?

• H_o : μ = 17, H_a : μ ≠ 19

• H_o : μ = 19, H_a : μ ≠ 19

• H_o : μ = 19, H_a : μ ≠ 17

• H_o : μ = 17, H_a : μ ≠ 17

Which of the following represents the appropriate null & alternative hypotheses?

The mean height of women is greater than 64"

• H₀: μ = 64"

  Hₐ: μ > 64"

• H₀: μ < 64"

  Hₐ: μ > 64"

• H₀: p > 64"

  Hₐ: p ≠ 64"

• H₀: p = 64"

  Hₐ: p > 64"