population standard deviations) are equal. This is hard to justify because of the lack of a strong
statistical test for the equality of population variances.Practice Problems
Multiple-Choice
A school district claims that the average teacher in the district earns $48,000 per year. The teachers’
organization argues that the average salary is less. A random sample of 25 teachers yields a mean
salary of $47,500 with a sample standard deviation of $2000. Assuming that the distribution of all
teachers’ salaries is approximately normally distributed, what is the value of the t -test statistic and
the P -value for a test of the hypothesis H 0 : μ = 48,000 against H (^) A : μ < 48,000?
a. t = 1.25, 0.10 < P < 0.15
b. t = –1.25, 0.20 < P < 0.30
c. t = 1.25, 0.20 < P < 0.30
d. t = –1.25, 0.10 < P < 0.15
e. t = –1.25, P > 0.25
Which of the following conditions is (are) necessary to justify the use of z -procedures in a
significance test about a population proportion?
I. The samples must be drawn from a normal population.
II. The population must be much larger (10–20 times) than the sample.
III. np 0 ≥ 5 and n (1 – p 0 ) ≥ 5.
a. I only
b. I and II only
c. II and III only
d. III only
e. I, II, and III
- A minister claims that more than 70% of the adult population attends a religious service at least once
a month. Let p = the proportion of adults who attend church. The null and alternative hypotheses you
would use to test this claim would be:
a. H 0 : p ≤ 0.7, H (^) A : p > 0.7
b. H 0 : μ ≤ 0.7, H (^) A : μ > 0.7
c. H 0 : p = 0.7, H (^) A : p ≠ 0.7
d. H 0 : p ≤ 0.7, H (^) A : p < 0.7
e. H 0 : p ≥ 0.7, H (^) A : p < 0.7
A t -test for the difference between two populations, means is to be conducted. The samples, of sizes
12 and 15, are considered to be random samples from independent, approximately normally
distributed, populations. Which of the following statements is (are) true?
I. If we can assume the population variances are equal, the number of degrees of freedom is 25.
II. An appropriate conservative estimate of the number of degrees of freedom is 11.