課程名稱︰統計學一下
課程性質︰必修
課程教師︰蔣明晃
開課學院：管理學院
開課系所︰工管系
考試日期（年月日）︰105/4/22
考試時限（分鐘）：160分鐘
試題 :
上機考題: (這部分是在電腦教室考的，時間緊湊，因此data檔來不及抓。)
考試時間:一節課
Part 1: Short answer questions by computer (20 points)
1. Discrimination in hiring has been illegal for many years. It is illegal to
discriminate against any person on the basis of race, gender, or religion. It
is also illegal to discriminate because of a person’s handicap if it in no
way prevents that person from performing job. In recent years, the definition
of “handicap” has widened. Several applicants has successfully sued
companies because they were denied employment for no other reason than that
they were overweight. A study was conducted to examine attitudes toward
overweight people. The experiment involved showing a number of subjects
videotape of an applicant being interviewed for a job. Before the interview,
the subject was given a description of a job. Following the interview, the
subject was asked to score the applicant in terms of how well the applicant
was suited for the job. The score was out of 100, where higher scores
described greater suitability. (The scores are interval data.) The same
procedure was repeated for each subject. However, the gender and weight
(average and overweight) of the applicant varied.
a. Can we infer that the scores of the four groups of applicants differ? (Use
the sheet 1 in the Excel file of XrA14-06) (5 points)
b. Are the differences detected in part (a) because of weight, gender, or
some interaction? (Use the sheet 2 in the Excel file of XrA14-06) (5 points)
(Note: Write down the null and alternative hypotheses, copy the complete
ANOVA Table from computer output, and answer the question to obtain full
credit)
2. The cost of workplace injuries is high for the individual worker, for the
company, and for society. It is in everyone’s interest to rehabilitate the
injured worker as quickly as possible. A statistician working for an
insurance company has investigated the problem. He believes that physical
condition is a major determinant in how quickly a worker returns to his or
her job after sustaining an injury. To help determine whether he is on the
right track, he organized an experiment. He took a random sample of male and
female workers who were injured during the preceding year. He recorded their
gender, their physical condition, and the number of working days until they
returned to their job. These data were recorded in the following way. Column
2 and 3 store the number of working days until return to work for men and
women, respectively. In each column, the first 25 observations relate to
those who are physically fit, the next 25 rows relate to individuals who are
moderately fit, and the last 25 observations are for those who are in poor
physical shape. Can we infer that the six groups differ? If differences
exist, determine whether the differences result from gender, physical
fitness, or some combination of gender and physical fitness. (10 points) (Use
the format of the SPSS file of XrA14-12) (Note: Write down the null and
alternative hypotheses, copy the complete ANOVA Table from computer output,
and answer the question to obtain full credit)
筆試時間:兩節課
II. Multiple Choices Questions: (30 points, 2 points for each question)
1. The quantity S_P^2 is called the pooled variance estimate of the common
variance of two unknown but equal population variances. It is the weighted
average of the two sample variances, where the weights represent the:
a. sample variances.
b. sample standard deviations.
c. degrees of freedom for each sample.
d. None of these choices.
2. In constructing a confidence interval estimate for the difference between
the means of two independent normally distributed populations, we:
a. pool the sample variances when the unknown population variances are equal.
b. pool the sample variances when the population variances are known and
equal.
c. pool the sample variances when the population means are equal.
d. never pool the sample variances.
3. When testing H_0:μ_1-μ_2=0 vs. H_1:μ_1-μ_2≠0 with the variances of both
populations known, the observed value of the z-score was found to be -2.15.
Then, the p-value for this test would be
a. .0158 b. .0316 c. .9842 d. .9684
4. Which of the following statement is correct regarding the percentile points
of the F-distribution?
a. F_(.05,10,20)=1/F_.95,10,20
b. F_(.05,10,20)=1/F_.05,20,10
c. F_(.95,10,20)=1/F_.05,20,10
d. F_(.95,10,20)=1/F_.95,20,10
5. In test for the equality of two population variances, when the
populations are normally distributed, the 10% level of significance has been
used. To determine the rejection region, it will be necessary to refer to the
F table corresponding to an upper-tail area of:
a. .90 b. .20 c. .10 d. .05
6. For testing the difference between two population proportions, the pooled
proportion estimate should be used to compute the value of the test statistic
when the:
a. populations are normally distributed.
b. sample sizes are small.
c. null hypothesis states that the two population proportions are equal.
d. samples are independently drawn from the populations.
7. In one-way ANOVA, the amount of total variation that is unexplained is
measured by the:
a. sum of squares for treatments.
b. degrees of freedom.
c. total sum of squares.
d. sum of squares for error.
8. In a completely randomized design for ANOVA, the numerator and denominator
degrees of freedom are 4 and 25, respectively. The total number of
observations must equal:
a. 24 b. 25 c. 29 d. 30
9. The value of the test statistic in a completely randomized design for ANOVA
is F=6.29. The degrees of freedom for the numerator and denominator are 5 and
10, respectively. Using an F table, the most accurate statements to be made
about the p-value is that it is:
a. greater than 0.05
b. between 0.001 and 0.010.
c. between 0.010 and 0.025
d. between 0.025 and 0.050
10. How does conducting multiple t-tests compare to conducting a single F-test?
a. Multiple t-tests increases the chance of a Type I error.
b. Multiple t-tests decreases the chance of a Type I error.
c. Multiple t-tests does not affect the chance of a Type I error.
d. This comparison cannot be made without knowing the number of populations.
11. In one-way analysis of variance, if all the sample means are equal, then the:
a. total sum of squares is zero.
b. sum of squares for treatments is zero.
c. sum of squares for error is zero.
d. sum of squares for error equals sum of squares for treatments.
12. Which of the following statement about multiple comparison methods is false?
a. They are to be use once the F-test in ANOVA has been rejected.
b. They are used to determine which particular population means differ.
c. There are many different multiple comparison methods but all yield the
same conclusions.
d. All of these choices are true.
13. The primary interest of designing a randomized block experiment is to:
a. reduce the within-treatments variation to more easily detect differences
among the treatment means.
b. increase the between-treatments variation to more easily detect
differences among the treatment means.
c. reduce the variation among blocks.
d. None of these choices.
14. How do you calculate the expected frequency for one cell in a
goodness-of-fit test?
a. The expected frequency is equal to the proportion specified in H_0 for
that cell.
b. Use the total number of observations divided by the number of categories.
c. Multiply the specified proportion for that cell (found in H_0) by the
total sample size.
d. None of these choices.
15. A chi-squared test of a contingency table with 6 degrees of freedom results
in a test statistic χ^2=13.58. Using the χ^2 tables, the most accurate
statement that can be made about the p-value for this test is that:
a. p-value > .10
b. p-value > .05
c. .05 < p-value < .10
d. .025 < p-value < .05
Ans: cabcd cddba bcacd
III. Short answer questions by hand calculation: (50 points)
1. Suppose that a random sample of 60 observations was drawn from a population.
After calculating the mean and standard deviation, each observation was
standardized and the number of observations in each of the intervals below
was counted. Can we infer at the 10% significance level that the data were
drawn from a normal population? (6 points)
Intervals Frequency
Z<=-1 8
-1<Z<=0 30
0<Z<=1 17
Z>1 5
2. A telemarketer makes five calls per day. A sample of 200 days gives the
frequencies of sales volumes listed below:
Number of Sales Observed Frequency (days)
0 10
1 38
2 69
3 63
4 18
5 2
Assume the population is binomial distribution with a probability of purchase
p equal to .50.
(a) Compute the expected frequencies for x= 0, 1, 2, 3, 4, and 5 by using the
binomial probability function or the binomial tables. Combine categories if
necessary to satisfy the rule of five. (6 points)
(b) Should the assumption of a binomial distribution be rejected at the 5%
significance level? (4 points)
3. In a completely randomized design, 12 experimental units were assigned to
the first treatment, 15 units to the second treatment, and 18 units to the
third treatment. A partial ANOVA table is shown below:
Source of Variation SS df MS F
Treatments * * * 9
Error * * 35
Total * *
(a) Fill in the blanks (identified by asterisks) in the above ANOVA table. (7
points)
(b) Test at the 5% significance level to determine if differences exist among
the three treatment means. (3 points)
4. In order to examine the differences in ages of health inspectors among five
counties, a Health Department statistician look random samples of six
inspectors’ ages in each county. The data are listed below. An F-test using
ANOVA showed that average age differs for at least two counties.
Ages of Inspectors among Five School Districts
1 2 3 4 5