IV . Because P < 0.01, we have grounds to reject the null hypothesis. We have strong evidence
that the two vaccines differ in their effectiveness. Although this was two-sided test, we note
that Vaccine A was less effective than Vaccine B.Rapid Review
A researcher reports that a finding of = 3.1 is significant at the 0.05 level of significance. What is
the meaning of this statement?
Answer: Under the assumption that the null hypothesis is true, the probability of getting a value at
least as extreme as the one obtained is less than 0.05. It was unlikely to have occurred by chance.
- Let μ 1 = the mean score on a test of agility using a new training method and let μ 2 = the mean score
on the test using the traditional method. Consider a test of H 0 : μ 1 – μ 2 = 0. A large sample
significance test finds P = 0.04. What conclusion, in the context of the problem, do you report if
(a) α = 0.05?
(b) α = 0.01?
Answer:
(a) Because the P -value is less than 0.05, we reject the null hypothesis. We have evidence that there
is a non-zero difference between the traditional and new training methods.
(b) Because the P -value is greater than 0.01, we do not have sufficient evidence to reject the null
hypothesis. We do not have strong support for the hypothesis that the training methods differ in
effectiveness.
True–False: In a hypothesis test concerning a single mean, we can use either z- procedures or t-
procedures as long as the sample size is at least 20.
Answer: False. With a sample size of only 20, we can not use z -procedures unless we know that the
population from which the sample was drawn is approximately normal and σ is known. We can use t -
procedures if the data do not have outliers or severe skewness, that is, if the population from which
the sample was drawn is approximately normal.
- We are going to conduct a two-sided significance test for a population proportion. The null
hypothesis is H 0 : p = 0.3. The simple random sample of 225 subjects yields = 0.35. What is the
standard error, s , involved in this procedure if
(a) you are constructing a confidence interval for the true population proportion?
(b) you are doing a significance test for the null hypothesis?
Answer:
(a) For a confidence interval, you use the value of in the standard error.Hence, (b) For a significance test, you use the hypothesized value of p . Hence,