Stats Final Study Guide Part 2
A normal distribution has a mean of μ = 70 with σ = 12. If one score is randomly selected from this distribution, what is the probability that the score will be greater than X = 58?
A. 0.8413
What is the value of SS (sum of squared deviations) for the following population? Population: 2, 3, 0, 5
A. 13
A population of N = 5 scores has ΣX = 20 and ΣX2 = 100. For this population, what is the value of SS (sum of squared deviations)?
A. 20
A sample of n = 25 scores has mean M = 20 and variance s2 = 9. What is the sample standard deviation?
A. 3
After every score in a sample is multiplied by 3, the mean is calculated and found to be M = 21. What was the mean for the original scores?
A. 7
Which of the following are requirements of a random sample?
A. Every individual has an equal chance of being selected.
A sample of n = 4 scores has a mean of M = 8. If one new score with a value of X = 3 is added to the sample, what will be the value for the new mean?
A. M=7.0
Scores on the SAT form a normal distribution with a mean of μ = 500 with σ = 100. If the state college only accepts students who score in the top 60% on the SAT, what is the minimum score needed to be accepted?
A. X=475
What term is used to identify the mean of the distribution of sample means?
A. the expected value of M
A normal distribution has a mean of μ = 100 with σ = 20. If one score is randomly selected from this distribution, what is the probability that the score will have a value between X = 80 and X = 100?
B. 0.1587
A jar contains 10 red marbles and 30 blue marbles. What is the probability of randomly selecting a red marble from the jar?
B. 10/40
For a sample with M = 80, a score of X = 88 corresponds to z = 2.00. What is the sample standard deviation?
B. 4
For a particular population, a sample of n = 9 scores has a standard error of 8. For the same population, a sample of n = 16 scores would have a standard error of ____.
B. 6
A sample of n = 6 scores has a mean of M = 5. One person with a score of X = 12 is added to the distribution. What is the mean for the new set of scores?
B. M=6
A normal distribution has a mean of μ = 80 with σ = 20. What score separates the lowest 30% of the distribution from the rest of the scores?
B. X=69.6
What happens to the standard error of M as sample size increases?
B. it decreases
A distribution is positively skewed. Which is the most probable order, from smallest to largest, for the three measures of central tendency?
B. mode, median, mean
A true/false test has 100 questions. Using the normal approximation to the binomial distribution, what is the probability of getting more than 55 correct by just guessing?
B. p(X > 55.5)
What term is used to describe the shape of a distribution in which the scores pile up on the left-hand side of the graph and taper off to the right?
B. positively skewed
What proportion of a normal distribution is located between the mean and z = 1.40?
C. 0.4192
A sample of n = 100 scores is selected from a population with μ = 80 with σ = 20. On average, how much error is expected between the sample mean and the population mean?
C. 2 points
A population of N = 6 scores has ΣX = 12 and ΣX2 = 54. What is the value of SS for this population?
C. 30
A sample of n = 4 scores has a standard error of 10 points. For the same population, what is the standard error for a sample of n = 16 scores?
C. 5
Samples of size n = 9 are selected from a population with μ = 80 with σ = 18. What is the standard error for the distribution of sample means?
C. 6
One sample has n = 4 scores and M = 10. A second sample has n = 6 scores and M = 5. If the two samples are combined, then what is the weighted mean for the combined sample?
C. 70/10 = 7.0
For a population with μ = 80 and σ = 10, what is the X value corresponding to z = -0.50?
C. 75
If all the possible random samples with n = 36 scores are selected from a normal population with μ = 80 and σ = 18, and the mean is calculated for each sample, then what is the average of all the sample means?
C. 80
If sample variance is computed by dividing SS by df = n - 1, then the average value of the sample variances from all the possible random samples will be ____ the population variance.
C. exactly equal to
What happens to the expected value of M as sample size increases?
C. it stays constant
A researcher measures eye color for a sample of n = 50 people. Which measure of central tendency would be appropriate to summarize the measurements?
C. mode
Which of the following symbols identifies the population standard deviation?
C. σ
John drives to work each morning and the trip takes an average of μ = 38 minutes. The distribution of driving times is approximately normal with a standard deviation of σ = 5 minutes. For a randomly selected morning, what is the probability that John's drive to work will take less than 35 minutes?
D. 0.2743
For a sample of n = 16 scores, how many scores are used to calculate the sample variance?
D. 16
For the population of scores shown in the frequency distribution table, the mean is ____. X f 5 2 4 1 3 3 2 2 1 2
D. 29/10 = 2.90
For a normal population with μ = 40 and σ = 10 which of the following samples has the highest probability of being obtained?
D. M = 44 for a sample of n = 100
What z-score values form the boundaries for the middle 60% of a normal distribution?
D. z = +0.84 and z = -0.84
You have a score of X = 65 on a math exam. The mean score for the class on the exam is μ = 70. Which of the following values for the standard deviation would give you the most favorable position within the class?
D. σ = 10
A population has μ = 50. What value of σ would make X = 55 a more central, representative score in the population?
D. σ = 20
Under what circumstances is a score that is 15 points above the mean an extreme score relatively far from the mean?
When the population standard deviation is much smaller than 15
On an exam with μ = 52, you have a score of X = 56. Which of the following values for the standard deviation would give you the highest position in the class distribution?
σ = 2
