Question

3)

A sample of midterm grades for five students showed the results: 72, 65, 82, 90, and 76. Based on the data, which of the following statements are correct, and which should be challenged as being too generalized? Justify your answer. a. The average midterm grade for the sample of five students is 77. b. The average midterm grade for all students who took the exam is 77. c. An estimate of the average midterm grade for all students who took the exam is 77. d. More than half of the students who take this exam will score between 70 and 85. e. If five other students are included in the sample, their grades will be between 65 and 90.

Answer 1

(a)

The average midterm grade for the sample of five students is 77.

The statement is correct.

Justification:

Sample average = (72 + 65 + 82 + 90 + 76)/5 = 385/5 = 77

(b)

The average midterm grade for all students who took the exam is 77

The statement should be challenged as being too generalized

Justification:

From the sample size of n = 5, such a generalization to the entire population is questionable.

(c)

An estimate of the average midterm grade for all students who took the exam is 77.

The statement is correct.

Justification:

Sample mean is the best estimate of population mean.

(d)

More than half of the students who take this exam will score between 70 and 85.

The statement should be challenged as being too generalized

Justification:

From the sample size of n = 5, such a generalization: More than half of the students who take this exam will score between 70 and 85: is questionable.

(e)

If five other students are included in the sample, their grades will be between 65 and 90.

The statement should be challenged as being too generalized

Justification:

The samples are random. Though Sample 1 data is between 65 and 90, another sample data also need not be between 65 and 90.