### Scientific Method And Research Study, Variance – Midterm Statistics

The key terms in these Statistic chapters include Variance, Scientific Method, Distribution, Hypothesis, Research Study, Distribution Table, Population, Weighted Average, Normal Distribution – Statistic

What the variance for the following sample of n = 3 scores? Scores: 1, 4, 7

**9**

For the scores in the following table, what is the value of ΣX 2? (X: 3,2,1 f: 1, 2, 4)

**21**

A set of scores ranges from a high of X = 45 to a low of X = 11. If these scores were placed in an appropriately designed grouped frequency distribution table, which of the following would be the bottom interval in the table?

**10-14**

Which statement below must be false regarding a distribution of scores?

**75% of the scores are above the median**

Which statement below is consistent with computing a weighted average of two individual samples?

**A computed weighted average will always be closer to the mean average of the larger sample than the mean average of the smaller sample.**

Jean Piaget observed his own children and developed a theory about the cognitive development of all children. What kind of reasoning was that?

**Inductive**

In the scientific method, the actual research study is not done until after the researcher has formed a hypothesis and made a specific prediction.

**True**

Quantitative research and qualitative research: what’s the difference?

**They generate different types of data**

Using observations of a small number of humans to Making a general statement about human behavior based on observations of a few people. What kind of reasoning is that?

**Inductive**

A population is normally distributed with µ = 86 and σ = 12. For this population, what is the 78 th percentile?

**X = 95.24**

Delores must grade a driver’s test completed by a group of training students. She knows that driver’s test scores are normally distributed with µ = 50 and σ = 6. Students are required to score in the top 75% of students on the test in order to pass the test and continue on with the training course. Which score do students need to obtain at a minimum in order to pass the test and continue with the course?

**X = 46**

What is the probability of randomly selecting a z-score less than z = -1.55 from a normal distribution?

**p = 0.0606**

A normal distribution has a mean of µ = 50 with σ = 6. If one score is randomly selected from this distribution, which is the probability that the score will be greater than X = 46?

**p = 0.7486**

A researcher is interested in whether a new reading technique influences the reading ability of elementary school children. The researcher knows that average reading ability among a population of third graders is µ = 3 with a standard deviation of σ = 1. If the researcher administers the new reading technique to a third grader who subsequently scores X = 4, it can be concluded that the new reading technique _____.

**Does not have an influence on reading ability.**

What the variance for the following sample of n = 3 scores? Scores: 1, 4, 7

**9**

For the scores in the following table, what is the value of ΣX 2? (X: 3,2,1 f: 1, 2, 4)

**21**

A set of scores ranges from a high of X = 45 to a low of X = 11. If these scores were placed in an appropriately designed grouped frequency distribution table, which of the following would be the bottom interval in the table?

**10-14**

Which statement below must be false regarding a distribution of scores?

**75% of the scores are above the median**

Which statement below is consistent with computing a weighted average of two individual samples?

**A computed weighted average will always be closer to the mean average of the larger sample than the mean average of the smaller sample.**

Jean Piaget observed his own children and developed a theory about the cognitive development of all children. What kind of reasoning was that?

**Inductive**

In the scientific method, the actual research study is not done until after the researcher has formed a hypothesis and made a specific prediction.

**True**

The distribution of z-scores corresponding with a population of scores always has a variance of _____.

**σ^2 = 1.**

A person scores X = 65 on an exam. Which set of parameters would give this person the worst grade on the exam relative to others?

**µ = 70 and σ = 5**

Which z-score corresponds to a score that is above the mean by 2 standard deviations?

**+2**

Which of the following statements must be false regarding a distribution of scores?

**No individual has a score exactly equal to the mode.**

One sample with n = 4 scores has a mean of M = 12, and a second sample with n = 6 scores has a mean of M = 8. If the two samples are combined, what is the mean for the combined set of scores?

**M = 9.6**

Which of the following symbols identifies the population standard deviation?

**σ**

Which symbol below identifies the sample variance?

**s^2**

Compute the interquartile range for the following scores that represent a continuous variable: 1, 2, 2, 2 4, 5, 10, 12

**3**

A frequency distribution graph represents frequencies associated with scores for a variable with vertical bars that have space between them. Which scale of measurement was used to measure this variable?

**Nominal**

A researcher surveys a sample of n = 20 college students and asks each person to identify their favorite movie. If the data were organized in a frequency distribution table, what would be included in the last column?

**List of frequencies**

A good hypothesis should make a positive statement about the existence of a relationship, a difference, or a treatment effect.

**True**

Which section of a research article can help you to develop ideas for studies by changing the characteristics of the participants or modifying the procedures for your own study?

**Method**

A birdwatcher puts several types of seed in her backyard to see which type attracts the most birds. Which method of acquiring knowledge is she using?

**Method of empiricism**

Observation, followed by hypothesis, followed by more observation. What’s going on?

**Scientific method**

Which proportion of a normal distribution is located between z = -1.75 and z = +1.75?

**0.9198**

A class consists of 10 male students and 30 female students. If one student is randomly selected from the class, what is the probability of selecting a male student?

**p = 10/40**

Which proportion of a normal distribution is located in the tail above z = +1.50?

**0.0668**

Which statement accurately describes the proportions in the body of a normal distribution?

**Body proportions are always ≥ .50.**

Which of the following symbols identifies the population standard deviation?

**σ**

Which symbol below identifies the sample variance?

**s^2**

Compute the interquartile range for the following scores that represent a continuous variable: 1, 2, 2, 2 4, 5, 10, 12

**3**

A researcher is interested in examining whether self-affirming oneself leads to decreased anxiety in response to threatening information. The researcher conducts a research study in which an individual is self-affirmed prior to receiving threatening information. Researchers know that on average individuals tend to have anxiety levels of µ = 10 with a standard deviation of σ = 2 when presented with this threatening information. If a self-affirmed individual has an anxiety level of X = 5 following the threatening message, it is reasonable to conclude that self-affirmation ______.

**Does have an influence on anxiety levels following threatening information.**

What the variance for the following sample of n = 3 scores? Scores: 1, 4, 7

**9**

For the scores in the following table, what is the value of ΣX 2? (X: 3,2,1 f: 1, 2, 4)

**21**

A set of scores ranges from a high of X = 45 to a low of X = 11. If these scores were placed in an appropriately designed grouped frequency distribution table, which of the following would be the bottom interval in the table?

**10-14**

Which statement below must be false regarding a distribution of scores?

**75% of the scores are above the median**

Which statement below is consistent with computing a weighted average of two individual samples?

**A computed weighted average will always be closer to the mean average of the larger sample than the mean average of the smaller sample.**

Jean Piaget observed his own children and developed a theory about the cognitive development of all children. What kind of reasoning was that?

**Inductive**

In the scientific method, the actual research study is not done until after the researcher has formed a hypothesis and made a specific prediction.

**True**

One sample with n = 4 scores has a mean of M = 12, and a second sample with n = 6 scores has a mean of M = 8. If the two samples are combined, what is the mean for the combined set of scores?

**M = 9.6**

A frequency distribution graph represents frequencies associated with scores for a variable with vertical bars that have space between them. Which scale of measurement was used to measure this variable?

**Nominal**

A researcher surveys a sample of n = 20 college students and asks each person to identify their favorite movie. If the data were organized in a frequency distribution table, what would be included in the last column?

**List of frequencies**

A good hypothesis should make a positive statement about the existence of a relationship, a difference, or a treatment effect.

**True**

Which section of a research article can help you to develop ideas for studies by changing the characteristics of the participants or modifying the procedures for your own study?

**Method**

A birdwatcher puts several types of seed in her backyard to see which type attracts the most birds. Which method of acquiring knowledge is she using?

**Method of empiricism**

Observation, followed by hypothesis, followed by more observation. What’s going on?

**Scientific method**

A person scores X = 65 on an exam. Which set of parameters would give this person the worst grade on the exam relative to others?

**µ = 70 and σ = 5**

The distribution of z-scores corresponding with a population of scores always has a variance of _____.

**σ^2 = 1.**

Using observations of a small number of humans to Making a general statement about human behavior based on observations of a few people. What kind of reasoning is that?

**Inductive**

What is the probability of randomly selecting a z-score less than z = -1.55 from a normal distribution?

**p = 0.0606**

Quantitative research and qualitative research: what’s the difference?

**They generate different types of data**

A good hypothesis should make a positive statement about the existence of a relationship, a difference, or a treatment effect.

**True**

Which section of a research article can help you to develop ideas for studies by changing the characteristics of the participants or modifying the procedures for your own study?

**Method**

A birdwatcher puts several types of seed in her backyard to see which type attracts the most birds. Which method of acquiring knowledge is she using?

**Method of empiricism**

**Method of empiricism**

Observation, followed by hypothesis, followed by more observation. What’s going on?

**Scientific method**

A person scores X = 65 on an exam. Which set of parameters would give this person the worst grade on the exam relative to others?

**µ = 70 and σ = 5**

The distribution of z-scores corresponding with a population of scores always has a variance of _____.

**σ^2 = 1.**

Which of the following symbols identifies the population standard deviation?

**σ**

Which symbol below identifies the sample variance?

**s^2**

Compute the interquartile range for the following scores that represent a continuous variable: 1, 2, 2, 2 4, 5, 10, 12

**3**