101年國立清華大學服務科學所(甲組)統計學

You have been asked by Hsinchu city council to estimate demographic information
about the population of Hsinchu. Due to cost and time limitations, you can only survey
100 residents. Among other things, you will need to measure the following variables:
ORIGIN (which city, township, or village a resident was born in), AGE (the age in
years of a resident), EDUCATION (how many years of formal education a resident has),
INCOME (yearly income of resident), and GENDER (male or female gender of
resident).

What kind of measurement scale do we need to use to measure ORIGIN?

nominal

ordinal

interval

ratio

You have been asked by Hsinchu city council to estimate demographic information
about the population of Hsinchu. Due to cost and time limitations, you can only survey
100 residents. Among other things, you will need to measure the following variables:
ORIGIN (which city, township, or village a resident was born in), AGE (the age in
years of a resident), EDUCATION (how many years of formal education a resident has),
INCOME (yearly income of resident), and GENDER (male or female gender of
resident).

Due to legal reasons, you are not permitted to interview residents who are less than 18
years old. How will this restriction affect the measurement of BORN?

increase bias

decrease bias

increase variance

decrease variance

Before interviewing residents of the city, you have pretested your interview instrument
on the students of a class you are taking - the class has 10 students in total. The
following are the ages (in years) of all students in the class: 19, 20, 21, 20, 20, 19, 20,
21, 19, 21.

 Approximately, what is the variance of AGE in this class?

0.66

1.00

0.60

1.50

0.77

none of the above

Before interviewing residents of the city, you have pretested your interview instrument
on the students of a class you are taking - the class has 10 students in total. The
following are the ages (in years) of all students in the class: 19, 20, 21, 20, 20, 19, 20,
21, 19, 21.

What should be the units of the variance of AGE?

no units

years

years 2

Before interviewing residents of the city, you have pretested your interview instrument
on the students of a class you are taking - the class has 10 students in total. The
following are the ages (in years) of all students in the class: 19, 20, 21, 20, 20, 19, 20,
21, 19, 21.

What are the approximate standardized values of AGE for the 10 students?

−1.00 , 0.00, 1.00, 0.00, 0.00, −1.00 , 0.00, 1.00, −1.00 , 1.00

−1.67 , 0.00, 1.67, 0.00, 0.00, −1.67 , 0.00, 1.67, −1.67 , 1.67

−2.36 , 0.00, 2.36, 0.00, 0.00, −2.36 , 0.00, 2.36, −2.36 , 2.36

−0.36 , 0.00, 0.36, 0.00, 0.00, −0.36 , 0.00, 0.36, −0.36 , 0.36

none of the above (explain)

Before interviewing residents of the city, you have pretested your interview instrument
on the students of a class you are taking - the class has 10 students in total. The
following are the ages (in years) of all students in the class: 19, 20, 21, 20, 20, 19, 20,
21, 19, 21.

What should be the units for the standardized values of AGE?

no units

years

years 2

After interviewing a sample of 100 residents of Hsinchu, you find that the mean AGE of
the sample respondents is 35 years with a standard deviation of 5.0, and that AGE
seems fairly normally distributed. However, you are told that the average ago of Taiwan
is larger than 35 years, and closer to 37 years. Based on your sample data, you need to
test whether the true average age of all Hsinchu residents is at least 37 years, or if it is
smaller than 37 years.

What are the most appropriate null and alternative hypotheses for this test?

Hnull : average age = 37 years

Halt : average age ≠ 37 years

Hnull : average age ≠ 37 years

Halt : average = 37

Hnull : average age = 37 years

Halt : average age < 37 years

Hnull : average age ≥ 37 years

Halt : average age < 37 years

After interviewing a sample of 100 residents of Hsinchu, you find that the mean AGE of
the sample respondents is 35 years with a standard deviation of 5.0, and that AGE
seems fairly normally distributed. However, you are told that the average ago of Taiwan
is larger than 35 years, and closer to 37 years. Based on your sample data, you need to
test whether the true average age of all Hsinchu residents is at least 37 years, or if it is
smaller than 37 years.

Calculate the t-value for the test to compare the average AGE found in your sample
against the claim described above. Use t = (ageave −μ ) /(s / n) .

1.000

2.165

4.000

3.965

2.000

1.956

After interviewing a sample of 100 residents of Hsinchu, you find that the mean AGE of
the sample respondents is 35 years with a standard deviation of 5.0, and that AGE
seems fairly normally distributed. However, you are told that the average ago of Taiwan
is larger than 35 years, and closer to 37 years. Based on your sample data, you need to
test whether the true average age of all Hsinchu residents is at least 37 years, or if it is
smaller than 37 years.

Reject Hnull at 0.001 significance

Reject Hnull at 0.050 significance

Reject Hnull at 0.100 significance

Cannot reject Hnull

The intercept term

Coefficient of AGE

Coefficient of EDUCATION

(A)Not significant (B)2.5%~5% (C)1%~2.5% (D) <1%

How would you interpret the estimate of the intercept:

The average income of all residents regardless of age or education

The minimum income of residents regardless of age or education

A random artifact of regression that has no meaning or units

None of the above (explain)

Predict the salary for a 23-year old resident with 18 years of education:

NTD 1,189,504

NTD 1,319,854

NTD 2,393,428

NTD 1,029,525