sample t -test.
E. Because np and n (1 – p ) are both at least 10, the student should use a two-proportion z -test.
Which of these is the best description of a P -value?
A. The probability of making a Type I error.
B. The probability of making a Type II error.
C. The probability of rejecting the null hypothesis if it is, in fact, false.
D. The probability of getting a test statistic at least as extreme as the observed test statistic, if the
null hypothesis is true.
E. The probability of getting a test statistic at least as extreme as the observed test statistic, if the
null hypothesis is false.
A farmer who raises hens for egg production wants his eggs to have a mean mass of 56 grams. He
is considering the purchase of a different type of hen, so he took a random sample of 18 eggs laid by
this type of hen. The distribution of the masses is symmetric and mound-shaped with a mean of 54.1
grams and no outliers. The farmer conducted a t -test to see if there is evidence that the eggs from
these hens have a mean mass that is different from 56 g and got a test statistic of t = –1.973. If he
uses a 5% significance level, which is the correct conclusion and reason?
A. Because t is more extreme than ±1.96, he should reject the null hypothesis. He has convincing
evidence at the 5% significance level that the mean mass of eggs from these hens is different
from 56 grams.
B. Because t is less extreme than the critical value of t for 17 degrees of freedom, he should not
reject the null hypothesis. He does not have convincing evidence at the 5% significance level
that the mean mass of eggs from these hens is different from 56 grams.
C. Because t is less extreme than the critical value of t for 18 degrees of freedom, he should not
reject the null hypothesis. He does not have convincing evidence at the 5% significance level
that the mean mass of eggs from these hens is different from 56 grams.
D. Because t is more extreme than the critical value of t for 18 degrees of freedom, he should
reject the null hypothesis. He has convincing evidence at the 5% significance level that the
mean mass of eggs from these hens is different from 56 grams.
E. Because the sample mean was less than 56, he should use a one-sided alternative hypothesis.
Thus, t is more extreme than the critical value of t for 17 degrees of freedom and he should
reject the null hypothesis. He has convincing evidence at the 5% significance level that the
mean mass of eggs from these hens is different from 56 grams.
- An experiment is conducted in which the response variable is the average gain in participants’
performance in the long jump. A two-sample t -test with a 5% level of significance will be used to
analyze the results. If all else is kept the same, which of the following descriptions of a possible
change in procedure is true?
A. Change from equal size treatment groups to very different size treatment groups would increase
the power of the test.
B. Change from a 5% significance level to a 1% significance level would increase the power of
the test.
C. Taking more careful measurements to reduce variability in the response would increase the
power of the test.
D. Increasing the sample size would reduce the probability of a Type I error.