Unless otherwise specified,
use the 5% level of significance. Answer each question exactly in the form
in which it is asked (i.e., do not merely state that a result is significant
or not significant).
Be sure to think first
whether the quantities are discrete or continuous. Also think whether
a one-tailed or two-tailed test is needed.
1. A die is rolled 120 times. If 25 times a 3 is obtained, does this cause us to doubt that this is an honest die?
2. A coin is tossed
600 times.
a) If 325 heads are obtained, is this considered a significantly large
deviation from the expected number of heads?
b) Is this considered a significantly large number of heads?
3. From experience it is known that 20% of a certain kind of seed germinate. If in an experiment 60 out of 400 seed germinate, is this considered a significantly poor germination on the basis of the 1% level of significance?
4. It is known from long experience that 5% of certain articles produced are defective and have to be discarded. A new man who has produced 600 of these articles has made 42 defective articles. Does this cast doubt on the man's ability to perform the job?
5. At a university, student records kept over a period of many years indicate that 64% pass the entrance examination in mathematics. During the fall of 1959, of 400 freshman taking the test, 70% passed. Was this a significant improvement in the students' aptitude in mathematics?
6. If experience shows that 4% of all white males of exact age of 65 die within a year, and it is found that 55 such males of a group of 1000 actually die within a year, should the group be regarded as being essentially different from the general mass, using the 1% level of significance?
7. Of 64 offspring of a certain cross between guinea pigs, 8 are black and the other are not black. According to the genetic model, these numbers (black and not black) should be in the ratio of 3:13. Are the observed data consistent with the model at the 5% level of significance?
8. A standard medication reduces reports of post-operative pains in 80% of the patients treated. A new medication for the same purpose is tested. In at least how many patients out of 100 tested must the medication be effective so that is can be considered a superior medication at the 1% level of significance?
9. The height of adults in a certain town has a mean of 65.42 inches with a standard deviations of 2.32 inches. A sample of 144 adults living in the slum district is found to have a mean height of 64.83 inches. Does this indicate that the residents of the slums are significantly retarded in growth on the basis of the 1% level of significance?
10. A manufacturer of string has established from several years' experience that the string he manufacturers has a mean breaking strength of 15.9 pounds with a standard deviation of 2.3 pounds. A change is made in the manufacturing process, after which a sample of 64 pieces is taken, whose mean breaking strength is found to be 15.0 pounds with a standard deviation of 2.2 pounds. Does this mean that the new process has a significantly damaging effect on the strength of the string?
11. A car manufacturer claims that its cars use on the average 5.50 gallons of gasoline for each 100 miles. A salesman selling cars for the company test 35 cars for gasoline mileage and finds that the average consumption of gasoline for these 35 cars is 5.65 gallons for each 100 miles with a standard deviation of 0.35 gallons. Do these results cast doubt on the claim of the company (1% level)?
12. The daily wages
in a particular industry are normally distributed with a mean of $13.20
and a standard deviation of $2.50. If a company in this industry employing
40 workers pays these workers on the average $12.20, can this company be
accused of paying inferior wages at the 1% level of significance?