Significance Tests Review 2024

In hypothesis testing, what is the null hypothesis?

• a statement of what the experiment is trying to prove or show, by applying some kind of treatment on one or more variables.

• a statement of the probability of obtaining the experimental results purely by chance.

• a statement of the validity of the experiment

• a statement of no difference from what one would normally expect if there were no effect of the experimental treatment

• a statement of the relative effectiveness of a treatment applied to a randomly selected group of subjects

Which of the following statements correctly describes strong evidence for rejection of the null hypothesis?

• The experimental outcome yields a test statistic of 0.

• The experimental results are consistent with the statement contained in the null hypothesis.

• The experimental results obtained would be very unlikely if the null hypothesis were true.

• The value of the test statistic of one sample is different from the value of the test statistic obtained from a different sample from the same population.

• The p-value is 0.32.

Which of the following is a true statement?

• A well-planned hypothesis test should result in a statement either that the null hypothesis test is true or that it is false

• The alternative hypothesis is stated in terms of a sample statistic.

• If a sample is large enough, the necessity for it to be a simple random sample is diminished.

• When the null hypothesis is rejected, it is because it is not true.

• Hypothesis tests are designed to measure the strength of evidence against a null hypothesis.

A manufacturer claims that fewer than 5% of the goods he produces are defective. If, out of 200 items randomly selected from his production, 14 are found to be defective, check his claim using a hypothesis test with a .05 significance level. The null and alternative hypotheses for this test will be:

• H₀: p = 0.05 and H_a: p ≠ 0.05

• H₀: p = 0.05 and H_a: p < 0.05

• H₀: p = 0.07 and H_a: p ≠ 0.07

• H₀: p = 0.07 and H_a: p < 0.07

• H₀: p̂ = 0.05 and H_a: p̂ ≠ 0.05

In a test of H₀: p = 0.4 against H_a: p ≠ 0.4, a random sample of size 100 yields a test statistic of z = 1.28. The P-value of the test is approximately equal to

• 0.90

• 0.05

• 0.10

• 0.40

• 0.20

Which of the following is not a condition for performing a significance test about a population proportion?

• The data should come from a random sample or randomized experiment

• Both np₀ and n(1-p₀) should be at least 10.

• If you are sampling without replacement from a finite population, then you should sample no more than 10% of the population.

• The population distribution should be approximately Normal, unless the sample size is large.

• All of the above are conditions for performing a significance test about a population proportion.

A pharmaceutical company claims that 8% or fewer of the patients taking their new statin drug will have a heart attack in a 5-year period. In a government-sponsored study of 2300 patients taking the new drug, 198 have heart attacks in a 5-year period. Is this strong evidence against the company claim?

• Yes, because the P-value is 0.005657

• Yes, because the P-value is 0.086087

• No, because the P-value is only 0.005657

• No, because the P-value is only 0.086087

• No, because the P-value is over 0.10.

A significance test allows you to reject H₀ in favor of an alternative H_a at the 5% significance level. What can you say about significance at the 1% level?

• H₀ can be rejected at the 1% significance level

• There is insufficient evidence to reject H₀ at the 1% significance level

• There is sufficient evidence to accept H₀ at the 1% significance level

• H₀ can be rejected at the 1% significance level

• The answer can’t be determined from the information given.

In conducting a hypothesis test, the p-value is the

• Probability of obtaining a result as extreme or more extreme than the one obtained if the null hypothesis is true

• Significance level of the test

• Probability of making a Type I error

• Probability of making a Type II error

• Probability that the null hypothesis is true

A psychologist reports that the result of a hypothesis test was statistically significant at the 0.05 level. Which of the following is consistent with this statement?

• The significance level calculated was larger than 0.05

• The significance level calculated was smaller than 0.05

• The p-value calculated was larger than the significance level of 0.05

• The p-value calculated was smaller than the significance level of 0.05

• There was not enough information to make a decision