Download Introductory Statistics Homework Assignment 4 Chapter 7

Introductory Statistics
Homework Assignment 4 Chapter 7 and 8
Dr. Robert L. Randall.
Chapter 7
(1) A sampling distribution is a theoretical distribution of statistics that is obtained by selecting all of the
possible samples of a specific size from a population.
(a) True.
(b) False.
(2) A distribution of sample means is a theoretical distribution of __________ that is obtained by
selecting all of the possible samples of a specific size from a population, calculating the mean of each
sample, and plotting the distribution.
(a) Raw scores.
(b) Standard deviations.
(c) Variances.
(d) Means.
(e) None of these.
(3) The Central Limit Theorem is a mathematical proposition that provides a precise description of the
distribution that would be obtained if you selected every possible sample, calculated every sample
mean, and constructed the distribution of the sample mean.
(a) True.
(b) False.
(4) A sampling distribution (distribution of sample means) will approximate what shape, regardless of
the shape of the distribution of original scores?
(a) Positively skewed distribution.
(b) Negatively skewed distribution.
(c) Normal distribution.
(d) There is no way to know the shape of the sampling distribution.
(e) None of these are correct.
(5) Sampling distribution (distribution of sample means) almost perfectly normal, regardless of the
shape of the distribution of original scores, if: (1) Population from which the samples are selected is
normally distributed or (2) Number of scores in each sample is relatively large (around 30 or more).
(a) True.
(b) False.
(6) For any population with mean μ and standard deviation σ, the distribution of sample means for
sample size n will have a mean that is?
(a) Smaller than the population mean.
(b) Equal to the population mean.
(c) Greater than the population mean.
(d) There is no way to know the mean of the distribution of sample means.
(e) None of these are correct.
(7) For any population with mean μ and standard deviation σ, the distribution of sample means for
sample size n will have a standard deviation that is?
(a) Smaller than the population standard deviation.
(b) Equal to the population standard deviation.
(c) Greater than the population standard deviation.
(d) There is no way to know the standard deviation of the distribution of sample means.
(e) None of these are correct.
(8) For any population with mean μ and standard deviation σ, the distribution of sample means for
sample size n will have a standard deviation that is equal to:
(a) The population standard deviation (σ) divided by the square root of the sample size (n).
(b) The population variance (σ2) divided by the square root of the sample size (n).
(c) The population standard deviation (σ) divided by the sample size (n).
(d) The population variance (σ2) divided by the sample size (n).
(e) There is no way to know the variance of the distribution of sample means.
(9) For any population with mean μ and standard deviation σ, the distribution of sample means for
sample size n will have a variance that is equal to:
(a) The population standard deviation divided (σ) by the square root of the sample size (n).
(b) The population variance (σ2) divided by the square root of the sample size (n).
(c) The population standard deviation (σ) divided by the sample size (n).
(d) The population variance (σ2) divided by the sample size (n).
(e) There is no way to know the variance of the distribution of sample means.
(10) Standard deviation of a distribution of sample means is (technically) called the:
(a) Standard deviation.
(b) Standard error of the population (P).
(c) Standard error of the mean (M).
(d) None of these are correct.
(11) The standard error of the mean provides a measure of how much distance is expected on average
between a sample mean and the population mean.
(a) True.
(b) False.
(12) The Law of Large Numbers states that the larger the sample size (n), the less probable it is that the
sample mean will be close to the population mean.
(a) True.
(b) False.
(13) Population distribution of individual IQ scores (raw scores) has population mean of 100 and
population standard deviation of 16. Select a sample of size 4 (N = 4). What is the standard error of
the mean for this sampling distribution? Note: Round to no more than two decimal places.
(14) Population distribution of individual IQ scores (raw scores) has population mean of 100 and
population standard deviation of 16. Select sample of size 16 (N = 16). What is the standard error of
the mean for this sampling distribution? Note: Round to no more than two decimal places.
(15) Population distribution of individual IQ scores (raw scores) has population mean of 100 and
population standard deviation of 16. Select a sample of size 64 (N = 64). What is the standard error
of the mean for this sampling distribution? Note: Round to no more than two decimal places.
(16) Population distribution of individual IQ scores (raw scores) has population mean of 100 and
population standard deviation of 16. Select a sample of size 64 (N = 64). Out of all of the possible
sample means in this sampling distribution, what proportion of sample means will fall at or below a
value of 102.56? Note: Round to no more than two decimal places.
(17) The population distribution of individual IQ scores (raw scores) has population mean of 100 and a
population standard deviation of 16. You select a sample of size 64 (N = 64). Out of all of the
possible sample means in this sampling distribution, what proportion of sample means will fall at or
above a value of 102.56? Note: Round to no more than two decimal places.
(18) Population distribution of individual IQ scores (raw scores) has population mean of 100 and a
population standard deviation of 16. Select a sample of size 64 (N = 64). Out of all of the possible
sample means in this sampling distribution, what proportion of sample means will fall at or below a
value of 97.44? Note: Round to no more than two decimal places.
(19) Population distribution of individual IQ scores (raw scores) has population mean of 100 and a
population standard deviation of 16. Select a sample of size 64 (N = 64). Out of all of the possible
sample means in this sampling distribution, what proportion of sample means will fall at or above a
value of 97.44? Note: Round to no more than two decimal places.
(20) Population distribution of individual IQ scores (raw scores) has population mean of 100 and a
population standard deviation of 16. Select sample of size 64 (N = 64). Out of all possible sample
means in this sampling distribution, what proportion of sample means will fall between a value of
102.56 and a value of 97.44? Note: Round to no more than two decimal places.
(21) The population distribution of individual IQ scores (raw scores) has population mean of 100 and a
population standard deviation of 16. You select a sample of size 64 (N = 64). What range of values is
expected for the sample mean 80% of the time?
(a) 90.00 to 110.00
(b) 95.00 to 105.00
(c) 96.00 to 104.00
(d) 97.44 to 102.56
(e) None of these are correct.
(22) The population distribution of individual SAT scores (raw scores) has population mean of 500 and a
population standard deviation of 100. You select a sample of size 100 (N = 100). Out of all of the
possible sample means in this sampling distribution, what value will have 70% of the sample means
falling at or below it? Note: Round to no more than two decimal places.
(23) The population distribution of individual SAT scores (raw scores) has population mean of 500 and a
population standard deviation of 100. You select a sample of size 100 (N = 100). Out of all of the
possible sample means in this sampling distribution, what value will have 70% of the sample means
falling at or above it? Note: Round to no more than two decimal places.
(24) The population distribution of individual SAT scores (raw scores) has population mean of 500 and a
population standard deviation of 100. You select a sample of size 100 (N = 100). What range of
values is expected for the sample mean 40% of the time?
(a) 490.00 to 510.00
(b) 495.00 to 505.00
(c) 494.8 to 505.20
(d) 497.44 to 502.56
(e) None of these are correct.
Chapter 8
(25) In general, the null hypothesis (Ho) states:
(a) There is no difference (no effect).
(b) There is a difference (effect).
(c) Neither of these is correct.
(26) In general, the alternative hypothesis (H1) states:
(a) There is no difference (no effect).
(b) There is a difference (effect).
(c) Neither of these is correct.
(27) Which of the following is (are) true concerning a Type I error?
(a) The results lead a researcher to fail to reject a null hypothesis that is really false.
(b) The results lead a researcher reject a null hypothesis that is actually true.
(c) Is sometimes (informally) referred to as a “Missed Discover”.
(d) Is sometimes (informally) referred to as a “False Alarm”.
(e) Both (b) and (d) are correct.
(28) Which of the following is (are) true concerning a Type II error?
(a) The results lead a researcher to fail to reject a null hypothesis that is really false.
(b) The results lead a researcher reject a null hypothesis that is actually true.
(c) Is sometimes (informally) referred to as a “Missed Discover”.
(d) Is sometimes (informally) referred to as a “False Alarm”.
(e) Both (a) and (c) are correct.
(29) The probability of a Type I error {p(Type I error)} is equal to:
(a) 1 - α.
(b) α
(c) 1 – β
(d) β
(e) None of these are correct.
(30) The probability of making a correct decision when the null hypothesis is true is equal to:
(a) 1 - α.
(b) α
(c) 1 – β
(d) β
(e) None of these are correct.
(31) The probability of a Type II error {p(Type II error)} is equal to:
(a) 1 - α.
(b) α
(c) 1 – β
(d) β
(e) None of these are correct.
(32) The probability of making a correct decision when the null hypothesis is false is equal to:
(a) 1 - α.
(b) α
(c) 1 – β
(d) β
(33) The “Power of a Statistical Test” (Statistical Power) is equal to:
(a) 1 - α.
(b) α
(c) 1 – β
(d) β
(34) Which of the following have an effect on Statistical Power?
(a) Size of the treatment effect.
(b) Sample size.
(c) Alpha level.
(d) One-tailed versus two tailed.
(e) All of these are correct (a, b, c, and d).
(35) When the null hypothesis is rejected, it means that:
(a) The probability of that event is so large that we conclude that it could not have occurred by chance.
(b) The probability of that event is so small that we conclude that it could not have occurred by chance.
(c) The observed test statistic value is less than the critical value.
(d) The observed test statistic value is greater than or equal to the critical value.
(e) Both (b) and (d) are correct.
(36) The population distribution of individual SAT scores (raw scores) has population mean of 500 and a
population standard deviation of 100. You select a sample of size 100 (N = 100). Using a two-tailed
test (non-directional) and alpha equal to 0.05 (α = 0.05), at or beyond what value(s) would the
probability of a sample mean value be extremely rare?
(a) 480.4 and 519.6
(b) 483.55 or 516.45
(c) 474.24 and 525.76
(d) 476.74 or 523.26
(e) None of these are correct.
(37) The population distribution of individual SAT scores (raw scores) has population mean of 500 and a
population standard deviation of 100. You select a sample of size 100 (N = 100). Using a two-tailed
test (non-directional) and alpha equal to 0.01 (α = 0.01), at or beyond what value(s) would the
probability of a sample mean value be extremely rare?
(a) 480.4 and 519.6
(b) 483.55 or 516.45
(c) 474.24 and 525.76
(d) 476.74 or 523.26
(e) None of these are correct.
(38) The population distribution of individual SAT scores (raw scores) has population mean of 500 and a
population standard deviation of 100. You select a sample of size 100 (N = 100). Using a one-tailed
test (directional) and alpha equal to 0.05 (α = 0.05), at or beyond what value(s) would the probability
of a sample mean value be extremely rare?
(a) 480.4 and 519.6
(b) 483.55 or 516.45
(c) 474.24 and 525.76
(d) 476.74 or 523.26
(e) None of these are correct.
(39) The population distribution of individual SAT scores (raw scores) has population mean of 500 and a
population standard deviation of 100. You select a sample of size 100 (N = 100). Using a one-tailed
test (directional) and alpha equal to 0.01 (α = 0.01), at or beyond what value(s) would the probability
of a sample mean value be extremely rare?
(a) 480.4 and 519.6
(b) 483.55 or 516.45
(c) 474.24 and 525.76
(d) 476.74 or 523.26
(e) None of these are correct.
(40) In class I gave you FOUR STEPS for HYPOTHESIS TESTING (these roughly correspond with
what the textbook presents). What are the four steps (in the correct order)?
(a) (1) Write Hypotheses; (2) Set Criteria; (3) Collect /Analyze Data; (4) Make Decision.
(b) (1) Make Decision; (2); Collect / Analyze Data; Set Criteria; Write Hypotheses.
(c) (1) Collect / Analyze Data; Make Decision; Write Hypotheses; Set Criteria.
(d) (1) Set Criteria; Collect / Analyze Data; Make Decision; Write Hypotheses.
(e) None of these are correct.
Use the following information for the next two questions. The population distribution of individual IQ scores
(raw scores) has population mean of 100 and a population standard deviation of 16. A researcher wrote a
book that she claims will significantly raise IQ scores. The researcher selects a sample of size 64 (N = 64) in
order to test the research hypothesis (alternative hypothesis) that her book will have a significant effect on IQ
scores (change them in either direction – raise or lower IQ scores). The researcher wants to maximize the
power of this statistical test.
(41) What is the null hypothesis for this test?
(a) Ho: μ = 100.
(b) Ho: μ ≠ 100.
(c) Ho: μ > 100.
(d) Ho: μ ≥ 100.
(e) Ho: μ < 100.
(42) What is the alternative hypothesis for this test?
(a) Ho: μ = 100.
(b) Ho: μ ≠ 100.
(c) Ho: μ > 100.
(d) Ho: μ ≥ 100.
(e) Ho: μ < 100.
Use the following information for the next two questions. The population distribution of individual SAT
scores (raw scores) has population mean of 500 and a population standard deviation of 100. A researcher
wrote a book that she claims will significantly raise SAT scores. The researcher selects a sample of size 400
(N = 400) in order to test the research hypothesis (alternative hypothesis) that her book will have a significant
effect on SAT scores (change them in either direction – raise or lower SAT scores). The researcher has the
400 students each read her book and then take the SAT exam. The mean SAT exam score for this sample is
514. The researcher wants to minimize the probability of a Type I error for this statistical test.
(43) What is the null hypothesis for this test?
(a) Ho: μ = 500.
(b) Ho: μ ≠ 500.
(c) Ho: μ > 500.
(d) Ho: μ ≥ 500.
(e) Ho: μ < 500.
(44) What is the alternative hypothesis for this test?
(a) Ho: μ = 500.
(b) Ho: μ ≠ 500.
(c) Ho: μ > 500.
(d) Ho: μ ≥ 500.
(e) Ho: μ < 500.
(45) What is the correct alpha level and “tailedness” for this test?
(a) Alpha equals 0.01, one-tailed.
(b) Alpha equals 0.01, two-tailed.
(c) Alpha equals 0.05, one-tailed.
(d) Alpha equals 0.05, two-tailed.
(e) Alpha equals 0.01, three-tailed.
(46) What is the correct value of the observed statistic for this test? Note: Round to no more than two
decimal places.
(47) What is the correct critical value for this test? Note: round to three decimal places.
(48) What is the correct decision for this test?
(a) Reject the alternative hypothesis.
(b) Fail to Reject the alternative hypothesis.
(c) Reject the null hypothesis.
(d) Fail to Reject the null hypothesis.
(e) None of these are correct.
(49) Describe the results in “plain English”?
(a) The book significantly raises SAT scores.
(b) The book significantly lowers SAT scores.
(c) The book has not effect on SAT scores.
(d) It is impossible to know the effect of the book on SAT scores.
(e) None of these are correct.
(50) What is the effect size (Cohen’s d) for this test? Note: Round to two decimal places.