### Sample Size, Shape of The Distribution, The Mean, Variance, Statistic Exam

The key terms in these Statistic chapters include Sample Size, The Mean, Central Tendency, Effect Size, Sample Mean, Standard Deviation, Population Mean, Measure Of Central Tendency, Distribution, Probability, Z Score, Sample, Variance, Population, Statistics Exam.

As sample size ____, the shape of the distribution becomes ____ likes a normal curve

Increase, more
decreases, less

z table

##### Benefits form standardizationProvides percentage of scores between the mean of distribution and given z score

A z score of 1. 25 represents an observation that is
a. 1.25 standard deviations below the mean
b. 0.25 standard deviations above the mean of 1
c. 1.25 standard deviations above the mean
d. both b and c

The effect size (d) is
a. the size of difference between the means
b. the size of the samples you use
c. the difference between the means scaled by the size of the standard deviation
d. the width of the distribution

In one-sample tests of means are
a. compare one sample mean with another
b. compare one sample mean against a population mean
c. compare two sample means with each other
d. compare a set of population means

What is the variance for the following population of scores? Scores: 2, 5, 6, 3

#### 2.50

The standard deviation of a sampling distribution is known as
a. the standard error
b. the variance
c. error
d. sampling deviation

Which of the following is NOT part of the Central Limit Theorem?
a. the mean of the sampling distribution approaches the population mean
b. the variance of the sampling distribution approaches the populations variance divided by the sampling size
c. the sampling distribution will approach a normal distribution as the sample size increases
d. all the above are part of the CLT

Sometimes we reject the null hypothesis when it is true. This is technically referred to as
a. Type 1 error
b. Type 2 error
c. a mistake
d. good fortune

If we were to repeat an experiment a large number of times and calculate a statistic such as the mean for each experiment, the distribution of these statistics would be called
a. the distributional distribution
b. the error distribution
c. the sampling distribution
d. the test outcome

The term “effect size” refers to
a. how large the resulting t statistic is
b. the size of the p value, or probability associated with that t
c. the actual magnitude of the mean or difference between means
d. the value of the null hypothesis

As sample size ____, the shape of the distribution becomes ____ likes a normal curve

z table

##### Benefits form standardizationProvides percentage of scores between the mean of distribution and given z score

A z score of 1. 25 represents an observation that is
a. 1.25 standard deviations below the mean
b. 0.25 standard deviations above the mean of 1
c. 1.25 standard deviations above the mean
d. both b and c

The effect size (d) is
a. the size of difference between the means
b. the size of the samples you use
c. the difference between the means scaled by the size of the standard deviation
d. the width of the distribution

In one-sample tests of means are
a. compare one sample mean with another
b. compare one sample mean against a population mean
c. compare two sample means with each other
d. compare a set of population means

If we compute 95% confidence limits on the mean as 112.5-118.4, we conclude that
a. the probability is 0.95 that the sample mean lies between 112.5 and 118.4
b. the probability is 0.05 that the population mean lies between 112.5 and 118.4
c. an interval computed in this way has a probability of 0.95 of bracketing the population mean
d. the population mean is not less than 112.5

On an exam with a mean of µ = 70, a person scores X = 60. Which of the following values for the standard deviation would position this person highest within the class?

#### σ = 15

A type 2 error is the probability of
a. finding a difference that is really there
b. finding a different that is not really there
c. not finding a difference that is really there
d. not finding a difference that is not really there

The standard error of the mean is

a. equal to the standard deviation of the population
b. larger than the standard deviation of the population
c. the standard deviation of the sampling distribution of the mean
d. none of the above

Imagine that your statistics prof lost all records of students raw scores on a recent test. However, she did record z-scores for the test as well as the class average of 48 out of 60 points and the SD of 4 points. She informs you your z-score is 0.95

a. what was your percentile score on this test?

b. using what you know about z scores and percentiles, how did you do on this test?

c. what was your original test score?

##### a. 83%b. the mean of the class was in the 80th percentiles. I did better than the rest of the class. I was 83% better than rest of classc. 86.3%

If the variance for a sample is computed and it is found to be rather large, the numbers in the sample are:

Widely spread out around the mean.

z score formula

(X-mean)/standard deviation

Formula to find x (with z score)

Mean + (z score)(standard deviation)

Transforming a set of scores into a standardized distribution of z-scores consists of graphically _____ the scores.

Relabeling

What is the variance for the following population of scores? Scores: 2, 5, 6, 3

#### 2.50

On an exam with a mean of µ = 70, a person scores X = 60. Which of the following values for the standard deviation would position this person highest within the class?

#### σ = 15

Calculate the effect size given the following info and describe the size of the effect

a. mu1 = 30, mu2 = 35, sigma =3

b. mu1 = 40, mu2 = 30, sigma = 10

c. mu1 = 100, mu2 = 98, sigma = 5

a. 1.67 – very large effect size

b. 1 – large effect size

c. 0.4 – small effect size

A researcher thinks that people who drive red cars drive faster than people who drive white cars. He recorded the speed of a random sample of red and white cars on the highway. The data follows. What is the 95% confidence interval for the true difference in speed?

Need to recalculate

What is the shape of the distribution for the following set of data? Scores: 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5

Positively skewed

Consider a 100-point college exam for which there is a large number of students that perform extremely well, as well as a large number of students that perform extremely poorly. Which statement below is true?

The distribution of scores is probably bimodal.

What is the preferred measure of central tendency for scores measured on an ordinal scale?

The median

Bimodal distribution has

#### 2 modes

For a data set that is skewed due to outliers, what is the most appropriate statistic of central tendency to use?

Median

What does SS stand for (in the context of statistics)?

Sum of squared deviations from the mean

Your sample data set has 4 scores in it. You calculate SS = 28. What is the variance?

#### 7

The standard deviation (SD) is most commonly used to get a sense of how far the typical score of a distribution differs from the mean. In computing the SD, why is it necessary to square the deviations from the mean for each score?

The mean of the unsquared deviations balances out to zero due to negative and positive values.

The ________ is equal to the square root of the ________.

Standard deviation; variance

Suppose we have a set of sample data and we compute the standard deviation to be 5.50. This means that the numbers in the sample generally deviate:

5.50 units from the mean

Rasheed and Xavier are examining the GRE math scores of the 25 graduate students in their statistics class to see the variability. They found the variance to be 1296. What is the standard deviation?

##### 36

If the variance for a sample is computed and it is found to be rather large, the numbers in the sample are:

Widely spread out around the mean.

z score formula

(X-mean)/standard deviation

Formula to find x (with z score)

Mean + (z score)(standard deviation)

Transforming a set of scores into a standardized distribution of z-scores consists of graphically _____ the scores.

Relabeling

What is the variance for the following population of scores? Scores: 2, 5, 6, 3

#### 2.50

On an exam with a mean of µ = 70, a person scores X = 60. Which of the following values for the standard deviation would position this person highest within the class?

#### σ = 15

The term “effect size” refers to
a. how large the resulting t statistic is
b. the size of the p value, or probability associated with that t
c. the actual magnitude of the mean or difference between means
d. the value of the null hypothesis

As sample size ____, the shape of the distribution becomes ____ likes a normal curve

increase, more
decreases, less

z table

Benefits form standardization
Provides percentage of scores between the mean of distribution and given z score

A z score of 1. 25 represents an observation that is
a. 1.25 standard deviations below the mean
b. 0.25 standard deviations above the mean of 1
c. 1.25 standard deviations above the mean
d. both b and c

The effect size (d) is
a. the size of difference between the means
b. the size of the samples you use
c. the difference between the means scaled by the size of the standard deviation
d. the width of the distribution

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