Data Analysis

1.  A probability is defined as . . .

1. The likelihood that a certain even will occur
2. The correlational relationship existing between two categorical variables
3. The causal relationship existing between two categorical variables
4.  empirical likelihood of the mean acting as a statistically significant predictor

What is the technique used by scientists to standardize the normal curve?

1.  Converting the probabilities into basic percentages so the curve can be streamlined, facilitating further analyses
2. Applying the standardized probability means to each curve
3. Converting a distribution’s raw scores to z-scores
4. There is no functional means of standardization for the normal curve

  The standard normal curve has an area of . . .

1. 1.00
2. 0
3. 0.50
4. 2.00

    The standard normal curve always has a mean of . . .

1. 1
2. 0
3. -1
4.  2

   If a z-score is negative, then the area associated with that score will also be negative.

1. True
2. False

An empirical distribution consisting of raw scores taken from a population is referred to as what by research scientists?

1. A sample distribution
2. The standard normal curve
3. A population distribution
4. The t distribution

   Approximately 68% of a sample falls within one and negative one standard deviation from the mean.

1. True
2. False

The central limit theorem states . . .

1. That whenever descriptive statistics are to be computed the sample statistic must exceed the sampling distribution mean
2. Prior to the calculation of inferential statistics, basic descriptive results must be generated to act as a bridge between the theoretical distributions and the empirical observations
3. Prior to the calculation of descriptive statistics, an infinite number of large samples must be drawn from the population under study, thus ensuring a normally distributed sample
4. That any time descriptive statistics are computed from an infinite number of large samples the resulting sampling distribution will be normally distributed

  Which of the following is an important distinction between the z and t distributions?

1.  The t distribution changes shape depending on sample size; the z distribution does not
2. The t distribution does not differ from the z distribution; it is simply another theoretical construct available for use by research scientists
3. The z distribution changes shape depending on sample size; the t distribution does not
4. The z distribution is normally distributed, whereas the t distribution is skewed

Which of the following is true of probabilities?

1. A probability varies from 0 to 1.0.
2. A 0 probability implies something is possible.
3. 1.0 probability implies something is impossible.
4. None of the above

 The probability of rolling a 4 on one toss of a standard six-sided die is:

1. .1
2. .167
3. 1.67
4. .25

The probability of rolling a 4 or a 6 on one toss of a standard six-sided die is:

1. .333
2. .409
3. .028
4. .167

The probability of rolling a 4 on one toss of a standard six-sided die and a 6 on a second toss is:

1. .334
2. .409
3. .028
4. .169

Which of the following is true of the normal distribution?

1. The normal distribution is symmetrical.
2. The normal distribution is unimodal.
3. The tails extend indefinitely in either direction.
4. All of the answers are true.

  Which of the following is NOT true of the normal curve?

1. It is skewed.
2. It is a probability distribution
3. Its total area contains 100% of the cases.
4. The mode, median, and mean are identical.

  Roughly ______% of the total area under the normal curve rests between two standard deviations above and below the mean.

1. 68
2. 47
3. 99
4. 95

17. In a symmetrical distribution, what percent of the scores fall above the mean?

1. 34%
2. 68%
3. 95%
4. 50%

The difference between the sample mean and the population mean is called:

1. mean variance.
2. sample variance.
3. sampling error.
4. population variance.

19. Which of the following is true of the sampling distribution?

1. The sampling distribution approximates the normal curve.
2. The mean of a sampling distribution is equal to the population mean.
3. The standard deviation of a sampling distribution is smaller than the standard deviation of the population.
4. All of the answers are correct.

20. The standard error of the mean is:

1. the same as the sample standard deviation.
2. the same as the population standard deviation.
3. the standard deviation of a theoretical sampling distribution.
4. equal to the sample size minus 1.

Question #1 (10 points)

Criminologists have long thought that living in a “broken home” (i.e., non-two-parent home) is a strong risk factor for delinquency. The following cross-tabulation shows the joint distribution of family structure with self-report delinquent status. Use this table to answer the question below.

Compute the probability of delinquency conditional on living with two parents, a single mother, and no mother figure. Note that you will compute three probabilities.

Question #2

Compute a standard score for a score of 25 in which the mean is 22 and the standard deviation is 2.5.

Question #3.

The following data show a contingency table of the association between political affiliation and support for the death penalty. Answer the following questions using this table.

1. What fraction of the sample opposes the death penalty?

1. What fraction of the sample is Democrat?

Question #4.

In 2000, there were 6,498,562 adults under correctional supervision. During this same year, the U.S. adult (i.e., 18 or older) population was estimated to be 202,682,000.

Compute the probability that a randomly selected adult in the U.S. is under correctional supervision.

Question #5.

Suppose that state-level unemployment rates are normally distributed with mean 4.14 and standard deviation 1.04. Use these as your population values, and calculate the following probabilities.

1. What is the standard score for a raw score of 7.5?

1. What is the standard score for a raw score of 1.5?

Question #6. 

The percent of area beyond z = 1.44 is ___________.

Question 7 

The percent of TOTAL cases that have a z score less than or equal to 1.46 is_____.

Question  8

The probability of obtaining a score between z = -1.40 and the mean is _________.

Question #9.

The percent of area between the mean and z = 1.45 is ___________.