statistics. 20 questions
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Assignment6.docx
ASSIGNMENT #6
1. You want to randomly select a number between 1 and 10, using Microsoft Excel. Which function do you use?
|
a. |
RANK |
|
b. |
RAND |
|
c. |
RANDBETWEEN |
|
d. |
Microsoft Excel does not have these capabilities |
2. A population consists of 8 items. The number of different simple random samples of size 3 that can be selected from this population is
|
a. |
24 |
|
b. |
56 |
|
c. |
512 |
|
d. |
128 |
3. Whenever the population has a normal probability distribution, the sampling distribution of is a normal probability distribution for
|
a. |
only large sample sizes |
|
b. |
only small sample sizes |
|
c. |
any sample size |
|
d. |
only samples of size thirty or greater |
4. Which of the following sampling methods does not lead to probability samples?
|
a. |
stratified sampling |
|
b. |
cluster sampling |
|
c. |
systematic sampling |
|
d. |
convenience sampling |
5. The purpose of statistical inference is to provide information about the
|
a. |
sample based upon information contained in the population |
|
b. |
population based upon information contained in the sample |
|
c. |
population based upon information contained in the population |
|
d. |
mean of the sample based upon the mean of the population
|
6. As a rule of thumb, the sampling distribution of the sample proportion can be approximated by a normal probability distribution whenever
|
a. |
np |
|
b. |
n(1 - p) |
|
c. |
n |
|
d. |
none of these alternatives is correct |
Answer questions 7 and 8 based on the following:
A random sample of 10 examination papers in a course, which was given on a pass or fail basis, showed the following scores.
|
Paper Number |
Grade |
Status |
|
1 |
65 |
Pass |
|
2 |
87 |
Pass |
|
3 |
92 |
Pass |
|
4 |
35 |
Fail |
|
5 |
79 |
Pass |
|
6 |
100 |
Pass |
|
7 |
48 |
Fail |
|
8 |
74 |
Pass |
|
9 |
79 |
Pass |
|
10 |
91 |
Pass |
7. The point estimate for the mean of the population is
|
a. |
750 |
|
b. |
100 |
|
c. |
85 |
|
d. |
75 |
8. The point estimate for the proportion of all students who passed the course is
|
a. |
0.8 |
|
b. |
0.2 |
|
c. |
1.8 |
|
d. |
1.2 |
9. A sample of 24 observations is taken from a population that has 150 elements. The sampling distribution of is
|
a. |
approximately normal because is always approximately normally distributed |
|
b. |
approximately normal because the sample size is large in comparison to the population size |
|
c. |
approximately normal because of the central limit theorem |
|
d. |
normal if the population is normally distributed |
10. A population has a mean of 75 and a standard deviation of 8. A random sample of 800 is selected. The expected value of is
|
a. |
8 |
|
b. |
75 |
|
c. |
800 |
|
d. |
none of these alternatives is correct |
11. A sample of 92 observations is taken from an infinite population. The sampling distribution of is approximately
|
a. |
normal because is always approximately normally distributed |
|
b. |
normal because the sample size is small in comparison to the population size |
|
c. |
normal because of the central limit theorem |
|
d. |
none of these alternatives is correct |
Answer questions 12 - 14 based on the following:
Consider a population of five families with the following data representing the number of children in each family.
|
Family |
# Children |
|
A |
2 |
|
B |
6 |
|
C |
4 |
|
D |
3 |
|
E |
1 |
12. Determine the sampling distribution of for n = 2 (recall our discussion of how to generate a sampling distribution of ). You should record your results in a frequency table. How many unique values does your random variable take on?
|
a. |
5 |
|
b. |
8 |
|
c. |
16 |
|
d. |
10 |
13. Refer to Question 12. Compute the expected value of .
|
a. |
3.2 |
|
b. |
6 |
|
c. |
8 |
|
d. |
1 |
14. State whether or not your results in Question 13 support the following statement: “ is an unbiased estimator of μ”
|
a. |
support |
|
b. |
do not support |
Answer questions 15 - 16 based on the following:
The average score for female golfers is 106. Use this value as the population mean and assume that the population standard deviation is 14 strokes.
15. A simple random sample of 45 female golfers is taken. What is the probability that the sample mean is within 3 strokes of the population mean for the sample of female golfers?
|
a. |
0.758 |
|
b. |
0.166 |
|
c. |
0.850 |
|
d. |
0.379 |
|
e. |
0.500 |
16. Assume that female golf scores are distributed normally. What is the probability that a randomly selected female golfer’s score is within 3 strokes of the population mean?
|
a. |
0.758 |
|
b. |
0.166 |
|
c. |
0.850 |
|
d. |
0.379 |
|
e. |
0.500 |
17. Random samples of size 100 are taken from an infinite population whose population proportion is 0.2. The mean and standard error of the proportion are
|
a. |
0.2 and 0.04 |
|
b. |
0.2 and 0.2 |
|
c. |
20 and 0.04 |
|
d. |
20 and 0.2 |
18. In a local university, 40% of the students live in the dormitories. A random sample of 80 students is selected for a particular study. The probability that the sample proportion (the proportion living in the dormitories) is between 0.30 and 0.50 is
|
a. |
0.4664 |
|
b. |
0.9328 |
|
c. |
0.0336 |
|
d. |
0.0672 |
19. A sample of 51 observations will be taken from an infinite population. The population proportion equals 0.85. The probability that the sample proportion will be between 0.9115 and 0.946 is
|
a. |
0.8633 |
|
b. |
0.6900 |
|
c. |
0.0819 |
|
d. |
0.0345 |
20. A population has a mean of 53 and a standard deviation of 21. A sample of 49 observations will be taken. The probability that the sample mean will be greater than 57.95 is
|
a. |
0 |
|
b. |
0.0495 |
|
c. |
0.4505 |
|
d. |
0.9505 |
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