Unit 9 Review - Significance Tests

• fail to reject,

  not convincing

• fail to reject, convincing

• reject,

  not convincing

• reject,

  convincing

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 >α , we fail to reject the null hypothesis. We do not have convincing evidence that the new method is better. 

The mean time it takes for a person to experience pain relief from aspirin is 25 minutes. A new ingredient is added to help speed up relief. Let µ denote the mean time to obtain pain relief with the new product. An experiment is conducted to verify if the new product works more quickly. What are the null and alternative hypotheses for the appropriate test of significance?

• H0 : µ = 25 vs. Ha : µ ≠ 25

• H0 : µ = 25 vs. Ha : µ < 25

• H0 : µ < 25 vs. Ha : µ = 25

• H0 : µ < 25 vs. Ha : µ > 25

• H0 : µ = 25 vs. Ha : µ > 25

Some people say that more babies are born in September than in any other month. To test this claim, you take a simple random sample of 150 students at your school and find that 21 of them were born in September. You are interested in whether the proportion born in September is higher than 1/12—what you would expect if September was no different from any other month. Thus your null hypothesis is H₀: p= 1/12. The P-value for your test is 0.0056. Which of the following

statements best describes what the P-value measures?

• The probability that September birthdays are no more common that any other month is 0.0056.

• The probability that September birthdays are more common is 0.0056

• Assuming September is no different from other months, there is 0.0056 probability of getting a sample with a proportion of September birthdays this far or farther above 1/12

• The probability of having a September birthday is 0.0056

We conduct a test to decide if people from Sweden are more likely to have blue eyes than people from England. Our p-value is 0.06 and our significance level is 0.05. What is the correct conclusion?

• Reject H₀

• Accept H₀

• Fail to reject H₀

• Accept H_a

Sally reads a newspaper report claiming that 12% of all adults in the U.S. are left-handed. She decides to test this claim. Sally selects a random sample of 55 classmates and finds that 9 were left-handed. Does this provide sufficient evidence that the proportion of lefties in Sally’s school is different than the national figure? Use α = 0.01.

Which is the correct p-value for this test?

• 0.160

• 0.319

• 0.508

• 0.492

The Quick Stop claims that the Big Slurp will contain 48

ounces of drink. You decide to test this claim because

you feel the actual amount is lower. Over the next few

weeks, you buy 50 Big Slurps and find the average

amount of drink is 47 ounces with a standard deviation

of 2.75 ounces. At α = 0.05, can you reject the Quick

Stop’s claim?

• Reject Ho

• Reject Ha

• Fail to reject Ho

• Fail to reject Ha

Sally reads a newspaper report claiming that 12% of all adults in the U.S. are left-handed. She decides to test this claim. Sally selects a random sample of 55 classmates and finds that 9 were left-handed. Does this provide sufficient evidence that the proportion of lefties in Sally’s school is different than the national figure? Use α = 0.01.

Which is the correct conclusion for this test?

• Since p-value = 0.319 < 0.01, I reject H₀. There is enough evidence to suggest a difference.

• Since p-value = 0.319 > 0.01, I reject H₀. There is enough evidence to suggest a difference.

• Since p-value = 0.319 > 0.01, I fail to reject H₀. There is not enough evidence to suggest a difference.

• Since p-value = 0.319 < 0.01, I fail to reject H₀. There is enough evidence to suggest a difference.