Confidence Intervals and Hypothesis Tests

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. 

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

• Since our p-value of 0.1317 is >undefined , 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 which has a mean of 17 pounds and want to know if they meet the weight specifications. What are the 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"

The mean monthly rent for one bedroom apartments in college towns around Michigan is $900. A future student group thinks that the rent is actually higher than the claim. To help them budget, the students determine the mean monthly rent of 200 different one bedroom apartments from around Michigan. State the null and alternative hypothesis for this test.

When p-value is greater than alpha we:

• Accept Ho
• Accept Ha
• Fail to reject Ho
• Reject Ho

A dairy association representative says 80% of people drink the milk after they eat the cereal. You believe the true proportion is less than 80%. Which are the correct hypotheses?

• Ho: p < .80 Ha: p = .80

• Ho: p = .80 Ha: p < .80

• Ho: everyone drinks the milk Ha: no one drinks the milk