Statistics Quiz (Education)

In educational research, observational studies are sometimes referred to as natural experiments. Explain what this means. Choose the correct answer below.

• In an observational study, students are assigned to different learning groups through random selection.

• In an observational study, a researcher measures characteristics of interest of a part of a student population but does not change existing conditions.

• In an observational study, students are paired up according to a similarity.

• In an observational study, a teaching method is applied to part of a student population and responses are observed.

Answer explanation

Observational studies, or natural experiments, involve researchers measuring characteristics of a population without altering conditions. This distinguishes them from experimental studies where treatments are applied.

Determine whether the variable is qualitative or quantitative. Explain your reasoning. Types of courses offered. The variable is (1) __________ because course types are (2) __________.

Answer explanation

The variable is (1) qualitative because places are (2) attributes or labels. They describe characteristics of locations rather than providing numerical values.

Identify the sampling technique used. An educational researcher randomly selected 30 schools from a list of all middle schools in the country and interviewed all of the teachers at each selected school.

• random

• stratified

• convenience

• cluster

• systematic

Answer explanation

The researcher used a cluster sampling technique by randomly selecting 30 middle schools (clusters) and interviewing all teachers within those selected schools, rather than sampling individual teachers across all schools.

In a classroom, the grade point averages of 10 students are recorded as follows. Determine the range of these GPAs. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8

• 2.8

• 3.2

• 1.4

• 2.45

Answer explanation

To find the range, subtract the minimum value (0.8) from the maximum value (4.0). Thus, 4.0 - 0.8 = 3.2. However, the range is often expressed as the difference between the highest and lowest values, which is 1.4.

In a classroom, the average score on a math test is 56 with a standard deviation of 4. If a student scored 64, what is the z-score of the student's test score?

• z = 1.07

• z = 2.00

• z = -1.07

• z = 1.75

Answer explanation

To find the z-score, use the formula z = (X - mean) / standard deviation. Here, z = (64 - 56) / 4 = 8 / 4 = 2.00. Thus, the correct answer is z = 2.00.

In a classroom, a teacher wants to form a committee of 5 students from a group of 7 students. The teacher realizes that the number of ways to choose 5 students is the same as choosing 2 students to be left out. Is the statement \( _7C_5 = _7C_2 \) true or false? Choose the correct answer below.

• This statement is false. A true statement is \( _7C_4 = _7C_2 \).

• This statement is false. A true statement is \( _2C_7 = 5C_7 \).

• This statement is false. A true statement is \( _7C_5 = _7P_2 \).

• This statement is true.

Answer explanation

The statement is false because \(_7C_5\) is not equal to \(_7C_2\). The correct relationship is \(_7C_5 = _7C_2\) due to the property \(_nC_k = _nC_{n-k}\), which gives \(_7C_5 = _7C_2\). A true statement is \(_7C_4 = _7C_2\).

Identify the two events described in the study and determine if the results indicate that the events are independent or dependent. Explain your reasoning. A study found that there is no relationship between students using digital textbooks and their academic performance. Identify the two events. Choose the correct answer below.

• Using digital textbooks and not using digital textbooks.

• Students' academic performance and not performing academically.

• Using digital textbooks and students' academic performance.

• Being in a classroom with digital textbooks and not being in a classroom with digital textbooks.

Answer explanation

The two events are being around satellite televisions and developing cancer. The study indicates no relationship between these events, suggesting they are independent, as exposure to satellite televisions does not affect cancer development.

Are the events independent or dependent in the context of education and teaching?

• Independent. A student's performance is related to the number of books in the library.

• Independent. The number of books in the library does not directly affect a student's performance.

• Dependent. The number of books in the library directly affects a student's performance.

• Dependent. The type of books available in the library determines a student's performance.

Answer explanation

The correct choice is 'Independent. Being around satellite televisions does not cause cancer.' This indicates that the occurrence of cancer is not influenced by exposure to satellite televisions, confirming their independence.

In a classroom, the probability that a student will pass a test is \( P(Pass) = 0.24 \). Find the probability that the student will not pass the test. The probability that the student will not pass the test is ______. (Simplify your answer.)

Answer explanation

The probability that an event will not happen is calculated as P(not E) = 1 - P(E). Given P(E) = 0.24, we have P(not E) = 1 - 0.24 = 0.76. Thus, the correct answer is 0.76.

In a classroom, a teacher tells the students that the probability of passing the exam is 148%. Explain why this statement is incorrect.

• The probability of an event must be contained in the interval [1,100].

• The probability of an event cannot exceed 100%.

• An event needs to have more than one possible outcome.

• The chance of passing is always more than 100%.

Answer explanation

The statement is incorrect because the probability of an event cannot exceed 100%. Probabilities are expressed as values between 0% and 100%, where 100% indicates certainty of the event occurring.