Question

Consider a population that consists of the 70 students enrolled in a statistics course at a large university. If the university registrar were to compile the grade point averages (GPAs) of all 70 students in the course and compute their average, the result would be a mean GPA of 2.98. Note that this average is unknown to anyone; to collect the GPA information would violate the confidentiality of the students’ academic records.

Suppose that the professor who teaches the course wants to know the mean GPA of the students enrolled in her course. She selects a sample of students who are in attendance on the third day of class. The GPAs of the students in the sample are:

3.71

3.92

3.68

3.60

3.64

3.27

3.93

3.12

3.40

3.74

1) The instructor uses the sample average as an estimate of the mean GPA of her students. The absolute value of the error in the instructor’s estimate is:

a) 0.52

b) 0.62

c) 0.86

d) 0.80

The portion of this error that is due to errors in data acquisition, nonresponse bias, and selection bias is referred to as 2) non sampling error/sampling error. This type of error is 3) more/less serious than 4) non sampling error/sampling error because taking a larger sample 5) will diminish/will not diminish its size or possibility of occurrence.

Suppose students in the university’s honors program are on a field trip on the third day of class. This may have introduced an 6) error in data acquisition/selection bias/a non response error/sampling error . Correcting this error will 7) sometimes/always/never bring the sample closer to the true mean GPA.

Suppose that the instructor incorrectly recorded the value 3.74 in the data and that the correct value is 3.47. This contribution to the error was caused by 8) error in data acquisition/selection bias/a non response error/sampling error. Given the instructor’s sample, correcting this error would bring the sample mean 9) Closer to the true mean GPA/Farther from the true mean GPA/To the exact value of the true mean GPA.

Suppose a student who was selected for the sample declines to disclose her GPA. This may have introduced 10) error in data acquisition/selection bias/a non response error/sampling error. Correcting this error will 11) sometimes/always/never bring the sample closer to the true mean GPA.

The professor suspects that her sample is flawed. She assigns each of the students in the class an ID number from 1 to 70 and uses Excel to select a simple random sample of ID numbers. The professor meets with the students in the sample. Each student signs a release that gives the registrar permission to use the student’s GPA to compute the sample average. The professor assures the students that the registrar will provide her with the average and not the GPAs of individual students.

The GPAs of the students in the new sample (from their academic records held by the registrar) are:

3.34

3.53

3.31

3.24

3.28

2.94

3.54

2.81

3.06

3.37

12) The professor uses the new sample average provided by the registrar as an estimate of the mean GPA of the students in the course. The absolute value of the error in her estimate is:

a) 0.42

b) 0.26

c) 0.01

d) 0.55

This error is 13) non sampling error/sampling error , and the only way to reduce its expected size is to 14) increase/decrease the sample size.

Answer 1

Solution :

given data,

The True mean GPA = 2.98

The sample is

3.71

3.92

3.68

3.60

3.64

3.27

3.93

3.12

3.40

3.74

xbar = (3.71+3.92+3.68+3.60+3.64+3.27+3.93+3.12+3.40+3.74 ) / 10

= 36.01 / 10

xbar = 3.601

Absolute erroe = Observed value - true value.

= 3.601 - 2.98

= 0.62

The portion of this error that is due to errors in data acquisition, nonresponse bias, and selection bias is referred to as non sampling error.

This type of error is more serious than sampling error because taking a larger sample will not diminish its size or possibility of occurrence.

Suppose students in the university’s honors program are on a field trip on the third day of class. This may have introduced an sampling error .

Correcting this error will always bring the sample closer to the true mean GPA.

Suppose that the instructor incorrectly recorded the value 3.74 in the data and that the correct value is 3.47. This contribution to the error was caused by an error in data acquisition. Given the instructor’s sample, correcting this error would bring the sample mean Closer to the true mean GPA.

Suppose a student who was selected for the sample declines to disclose her GPA. This may have introduced a non response error.

Correcting this error will sometimes bring the sample mean closer to the true mean GPA.

Sample error :- Difference between the sample and the population.

Non -Sample error :-

1. Covering error

2. Non response error

3. measurement error.

4. Data handling error.

Non-sampling error are more serious than sampling errors.

If we increase the sample sixe, the error (non sampling error) will not reduce.

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