PSYC 208 - Psychology Statistics
What are the real limits? 0.1
0.05 & 0.15
What are the real limits? 12.6
12.55 & 12.65
What are the real limits? 15.2
15.15 & 15.25
What are the real limits? 170.26
170.255 & 170.265
What are the real limits? 170.261
170.2605 & 170.2615
What are the real limits? 32
31.5 & 32.5
Notation: σ^2
Because the standard deviation is the square root of the variance, we write the variance of a population as σ^2
H0 is true --->
Fail to reject H0 Deciding independent variable had NO effect when it did NOT
Learning check #1 T/F: The computational & definitional formulas for SS sometimes give different results.
False
Learning check #11 True/False: Σx^2=(Σx)^2
False
Learning check #2 T/F You can determine how many individuals had each score from a grouped frequency distribution
False
Learning check #2 T/F: If all the scores in a data set are the same, the Standard Deviation is equal to 1.00.
False
Learning check #4 T/F Sample size has a great influence on measures of effect size
False
Learning Check #5 T/F For any negative z-scores, the tail will be on the right hand side
False - negative tale is on the left
H0 is false ---->
Reject H0 Deciding that independent variable had an effect when it did
Reject H0
Reject H0; which means that we say that there WAS AN EFFECT of the independent variable (IV) on the dependent variable (DV)
Retain (Fail to reject) H0
Retain (Fail to reject) H0; which means we say that the independent variable had NO EFFECT on the dependent variable.
Standard deviation formula
Standard deviation= √ (SS/N)
Learning Check #2 T/F By chance, two samples selected from the same population have the same size (n = 36) and the same mean (M = 83. They will also have the same t statistic.
True
Learning Check #3 T/F As sample size increases, the value of the standard error decreases
True
Learning Check #3 T/F For an independent measure t statistic, the estimated standard error measures how much difference is reasonable to expect between the sample means if there is no treatment effect
True
Learning check #12 True/False: (Σx)(Σx)=(Σx)^2
True
Learning check #2: T/F: A negative z-score always indicates a location below the mean
True
Learning check #3 T/F: It is possible for more than 50% of the scores in a distribution to have values above the mean.
True
Learning check #7 T/F: The mean and median have the same values, so the distribution is probably symmetrical
True
Learning Check #6 T/F A type I error is like convicting an innocent person in a jury trial
True - innocent is the "null hypothesis" for a jury trial; conviction is rejecting that hypothesis
Learning Check #5 T/F A report shows ANOVA results: F(2, 27)= 5.46, p<.05. You can conclude that the study used a total of 30 participants.
True because df total= N-1
Learning Check #10 T/F An effect that exists is less likely to be detected if σ is large
True- A larger standard deviation increases the standard error and produces a smaller z.
Learning Check #2 T/F If the size of the critical region decreases, the alpha level is decreased.
True- Alpha refers to the proportion of the area in the critical region
Learning check #1 T/F You can determine how many individuals had each score from a frequency distribution table
Ture
Variance formula
Variance= SS/N
1. A sample of n=20 scores ranges from a high of X=9 to a low of X=3. If these scores are placed in a frequency distribution table, how many X values will be listed in the first column? a) 7 b) 9 c) 20 d) 6
a) 7
2. For the following distribution of quiz scores, how many individuals took the quiz? X f 5 2 4 4 3 2 2 1 a)n=9 b) cannot be determined c)n=5 d)n=15
a)n=9
4. A population of N = 10 scores has a mean of µ = 80. If 5 points are added to every score in the distribution, what is the value of the new mean? a. still µ = 80 b. µ = 85 c. µ = 75 d. µ = 130
b. µ = 85
A set of scores ranges from a high of X =48 to a low of X = 7. If these scores are placed in a grouped frequency distribution table with an interval width of 5 points, the bottom interval in the table would be _______. a) 7-11 b) 5-10 c) 7-12 d) 5- 9
d) 5- 9
9. Last week Tom had exams in Statistics and in English. He scored 10 points above the mean on both exams. From this information, what can you conclude about the z-scores for Tom's two scores? Select one: a. None of the other choices is correct. b. Tom has identical z-scores for the two exams. c. Tom will have a higher z-score for the exam with the lower mean. d. Both of Tom's z-scores are positive.
d. Both of Tom's z-scores are positive.
7. In a population of N = 6, five of the individuals all have scores that are exactly 1 point above the mean. From this information, what can you determine about the score for the sixth individual? Select one: a. It is also above the mean by 1 point. b. There is not enough information to describe the 6th score. c. It is below the mean by 1 point. d. It is below the mean by 5 points.
d. It is below the mean by 5 points.
1. For any set of data, the sum of the deviation scores will always be _____. a. less than zero b. impossible to determine without more information c. greater than zero d. equal to zero
d. equal to zero
df's formula
degrees of freedom df= n-1
Statistic notation N
is the # of scores in a population
Statistic notations n
is the # of scores in a sample
Alpha level
level of significance, is a probability value used to define "very unlikely" Usually alpha is set at either .05 (as in the previous slide) .01 .001
Formula for standard deviation of sample
s=√(SS/(n-1))
formula for variance of sample
s^2= SS/ (n-1)
__ X
same as M; mean of a sample
Notation: s
standard deviation of sample
µ
the mean of a population
M
the mean of a sample
Notation: σ
the standard deviations of a population
Notation: s^2
variance of a sample
3 properties of standard scores
1. The mean of a set of z-scores is always zero 2. The SD of a set of standardized scores is always 1 3. The distribution of a set of standardized scores has the same shape as the unstandardized scores
Purpose of z-scores
1. identify and describe location of every score in the distribution. 2. Standardize an entire distribution -Sign tells whether score is located above or below the mean -Number tells distance between score and mean in standard deviation units
Learning check #3 True/False: When sample differs from the population there is a systematic difference between groups
False
Learning check #4 T/F: It is possible for more than 50% of the scores in a distribution to have values above the median
False
Learning check #6 T/F: The mean uses all the scores in the data, so it is the best measure of central tendency for skewed data.
False
Learning check #6 T/F If a researcher reports that t(6)= 1.98, p>.05, the H0 was rejected
False
Learning check #3: T/F:A score close to the mean has a z-score close to 1.00
False Scores close to 0 have z-scores close to 0.00
Learning Check #3 T/F Probability predicts what kind of population is likely to be obtained
False The population is given. Probability predicts what a sample is likely to be like
Learning Check #5 T/F A sample mean with z=3.00 is a fairly typical, representative sample
False - a z-score of 3.00 is an extreme, or unlikely, z-score
Learning Check #4 T/F Post tests are needed if the decision from an analysis of variance is to fail to reject the null hypothesis
False - post hoc tests are only needed when at lease one mean difference is significant
Learning Check #5 T/F the homogeneity assumption states that the 2 samples variance must be equal
False - the sample variances must be similar but not identical
H0
The Null Hypothesis -states that, in the general population, there is no change, no difference, or no relationship. -the Independent Variable (IV) had no effect on the Dependent Variable (DV). H0: µ Glutathione = µ population H0: µ Glutathione = 80
Learning check #2 True/False: Most research studies use data from samples
TRUE
H1
The Alternative Hypothesis -there is a change, a difference, or a relationship in the general population -the Independent Variable (IV) had and effect on the Dependent Variable (DV) H1: µ Glutathione ≠ µ population H1: µ Glutathione ≠ 80
Learning check #2 A sample of n = 7 scores has M= 5. All of the scores are doubled. What is the new mean? a. M=5 b. M=10 c. M=25 D. More information is needed to compute M
b. M=10
5. A population has SS = 30 and σ^2 = 6. How many scores are in the population? a. cannot be determined without additional information b. N = 5 c. N = 6 d. N = 180
b. N = 5 σ^2=SS/N 6=30/N N=5
3. A population with a mean of μ = 6 has ΣX = 42. How many scores are in the population? Select one: a. N = 252 b. N = 7 c. cannot be determined from the information given d. N = 6/42 = 1/7
b. N = 7
Statistic notations Σ
summation sign
the t-test for a single population is used to .....
to determine the effect of an independent variable on a dependent variable by comparing a sample mean to the mean of a hypothesized population using the t statistic
Four steps of Hypothesis Testing
1. State the hypotheses 2. Set the criteria for a decision 3. Collect data and compute sample statistics 4. Make a decision
Learning Check #2 T/F If both samples have n=10, the independent measures t statistic will have df=19
False should be 18
Learning Check #4 T/F When the z-score is quite large, it shows the null hypothesis is true.
False- A large z-score is in the critical region where H0 is unlikely
Learning Check #8 True/False Variables that cannot be measured directly are not real.
False- Constructs (internal states) can only be observed indirectly, but are the subject of much research
Learning check #5 True/False: All research methods have an independent variable
False- Correlational methods don't need an independent variable
Learning Check #5 T/F A decision to retain the null hypothesis means you showed that the treatment has no effect
False- Failing to reject H0 does not prove it true, just not enough evidence to reject it
Learning Check #2 T/F Choosing random individuals who pass by yields a random sample
False- Not all individuals pass by, so not all have an equal chance of being selected for the sample
Learning Check #6 True/False All research methods can show cause-and-effect relationships
False- Only experiments control the influence of participants and environmental variables
Learning Check#5 T/F When the value of the t statistic is near 0, the null hypothesis should be rejected
False- When the value of t is near 0 the difference between M and μ is also near 0
Learning Check #2 T/F If the null hypothesis is true, the F-ratio for ANOVA is expected (on average) to have a value of 0.
False- if the null hypothesis is true, the f-ratio will have a value near 1.00
Learning Check #6 T/F The mean of the sample is always equal to the population mean
False- individual samples will vary from the population mean
Learning Check #2 T/F The distribution of sample means is always normal shaped
False- it's normal shaped if the population is normal of n ≥ 30
Learning check #7 T/F A type II error is like convicting a guilty person in a jury trial
False- there is no error in convicting a guilty person in a trial
Learning check #8 T/F: A biased statistic has been influenced by researcher error
False: Bias refers to the systematic effect of using sample data to estimate a population parameter
Learning check #4 T/F: A treatment center for children measured the marital status of their parents (single, married, divorced, etc.) A histogram would be appropriate for these data.
False: Marital status is a nominal variable; a bar graph is needed
Learning check #6 T/F: The standard deviation is the distance from the Mean to the farthest point on the distribution curve
False: The standard deviation extends from the mean approximately halfway to the most extreme score
Type I Error
H0 is True ----> Reject H0 Deciding independent variable had effect when it did NOT
Type II Error
H0 is false ---> Fail to reject H0 Deciding that independent variable had NO effect when it did
Learning Check #6 T/F If you know the probability, you can find the corresponding z-score
True- Locate the proportion in the correct column and read the z-score from the left column
Learning Check #3 T/F Compared to a z-score, a hypothesis test with a t statistic requires less information about the population.
True- The t statistic does not require the population standard deviation; the z-test does.
Learning Check #9 T/F An effect that exists is more likely to be detected if n is large
True- a larger sample produces a smaller standard error and larger z
Learning Check #9 True/False: Research measurements are made using specific procedures defined ahead of time.
True- operational definitions assure consistent measurements and serve as definitions of constructs
Learning Check #1 T/F ANOVA allows researchers to compare several treatment conditions without conducting several hypothesis test
True- several conditions can be compared in one test
Learning Check #3 T/F The critical region defines unlikely values if the null hypothesis is true
True- this is the definition of "unlikely"
Learning check #9 T/F: On average, an unbiased sample statistic has the same value as a population parameter
True: Each sample's statistic differs from the population parameter, but the average of all samples will equal the parameter
Learning check #5 T/F A sample systematically has less variability than a population
True: Extreme scores affect variability, but are less likely to be included in a sample
Learning check #5 T/F: A treatment center for children measured the time they spent playing with other children (in minutes). A histogram would be appropriate for these data.
True: is measured continuously and is an interval variable
7. A researcher conducts a hypothesis test using a sample from an unknown population. If the t statistic has df = 35, how many individuals were in the sample? Select one: a. n = 36 b. n = 35 c. cannot be determined from the information given d. n = 34
a. n = 36
7. A sample of n = 20 scores is transformed into z-scores. What is the mean for the set of 20 z-scores? a. 0 b. 1 c. 10 d. cannot be determined without more information
a. 0
8. 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 less than X = 76? a. 0.6915 b. 0.3830 c. 0.1915 d. 0.3085
a. 0.6915
2. Which set of scores has the smallest standard deviation? a. 27, 105, 10, 80 b. 145, 143, 145, 147 c. 5, 11, 42, 22 d. 11, 17, 31, 53
a. 27, 105, 10, 80
3. A population of scores has µ = 80. In this population, a score of X = 86 corresponds to z = +2.00.What is the population standard deviation? a. 3 b. 12 c. 2 d. 6
a. 3 z= (x-µ)/σ 2=(86-80)/σ
4. For a sample with M = 80, a score of X = 88 corresponds to z = 2.00. What is the sample standard deviation? a. 4 b. 2 c. 16 d. 8
a. 4 z= (x-µ)/σ 2=(88-80)/σ
7. A population of scores has µ = 50 and σ = 12. If you subtract five points from every score in the population, then the new standard deviation will be _____. a. 7 b. insufficient information, cannot be determined c. 45 d. 12
a. 7 subtract 5 from σ
1. Probability values are always ______. a. All of the other 3 choices are correct b. greater than or equal to 0 c. positive #'s d. less than or equal to 1
a. All of the other 3 choices are correct
8. What happens to the standard error of M as sample size increases? Select one: a. It decreases b. It stays constant c. It also increases
a. It decreases
5. Which set of characteristics will produce the smallest value for the estimated standard error? Select one: a. a large sample size and a small sample variance b. a small sample size and a small sample variance c. a large sample size and a large sample variance d. a small sample size and a large sample variance
a. a large sample size and a small sample variance
5. In N = 25 games last season, the college basketball team averaged µ = 76 points with a standard deviation of σ = 6. In their final game of the season, the team scored 89 points. Based on this information, the number of points scored in the final game was _____. a. far above average b. above average, but it is impossible to describe how much above average c. There is not enough information to compare last year with the average. d. a little above average
a. far above average
Learning Check #7 Membership in MENSA requires a score of 130 on the Stanford-Binet 5 IQ test, which has μ = 100 and σ = 15. What proportion of the population qualifies for MENSA? a. p= 0.0228 b. p= 0.9772 c. p= 0.4772 d. p= 0.0456
a. p= 0.0228
9. What is the shape of the distribution for the following set of data? Scores: 1, 2, 2, 2, 2, 3, 3, 4, 5, 6 a. positively skewed b. symmetrical c. rectangular d. negatively skewed
a. positively skewed
9. Which of the following is true for a symmetrical distribution? a. the mean, median, and mode are all equal b. mean = mode c. median = mode d. mean = median
a. the mean, median, and mode are all equal
2. A researcher is measuring problem-solving times for a sample of n = 20 children. However, one of the children fails to solve the problem so the researcher has an undetermined score. What is the best measure of central tendency for these data? a. the median b. the mode c. the mean d. Central tendency cannot be determined for these data.
a. the median
What is required by the homogeneity of variance assumption? Select one: a. the two sample variances are equal. b. none of the other options is required by the homogeneity assumption. c. the two population variances are equal. d. the pooled variance has a value between the two sample variances.
a. the two sample variances are equal.
1. What is the value of ΣX+1 for the following scores? Scores 3,0,5,2 a) 14 b) 11 c) 32 D) 20
b) 11 (Take each of the #'s and add them together to =10 then +1=11)
3. Organizing a set of scores into a table or graph would be an example of using________. a) inferential statistic b) descriptive statistic c) population statistics d) sample statistics
b) descriptive statistic
Learning check #10 Σx^2+47 instructs you to .... a) square each score & add 47 up to it, then sum those #'s b) square each score, add up the squared scores, then add 47 to that sum c) add 47 to each score, square the result, and sum those #'s d) add up the scores, square that sum, and add 47 to it
b) square each score, add up the squared scores, then add 47 to that sum
7. What additional information is obtained by measuring on a interval scale compared to a ordinal scale? a) the direction of the differences b) the size of the differences c) whether the measurements are the same or different d) none of the above
b) the size of the differences
4. What proportion of a normal distribution is located between the mean and z = -0.40? Select one: a. 0.3108 b. 0.1554 c. 0.3446 d. 0.6554
b. 0.1554
9. 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 = 90 and X = 120? a. 0.2996 b. 0.5328 c. 0.4672 d. 0.1498
b. 0.5328
10. A skewed distribution typically has _____ distinct tail(s) and a normal distribution has ____ distinct tail(s). a. 1, 1 b. 1, 2 c. 2, 2 d. 2, 1
b. 1, 2
6. A random sample of n = 4 scores is selected from a population with µ = 80 and σ = 20. On average, how much difference would you expect between the sample mean and the population mean? Select one: a. 80 points b. 10 points c. 5 points d. 0 points (the sample mean should be the same as the population mean)
b. 10 points
Learning Check #1 A population has μ = 60 with σ = 5. The mean of distribution of sample means for samples of size n = 4 selected from this population would have an expected value of _____. a. 5 b. 60 c. 30 d. 15
b. 60
Learning check #1: A z-score of z = +1.00 indicates a position in a distribution ____ a. Above the mean by 1 point b. Above the mean by a distance equal to 1 standard deviation c. Below the mean by 1 point d. Below the mean by a distance equal to 1 standard deviation
b. Above the mean by a distance equal to 1 standard deviation
10. A sample with M = 85 and s = 12 is transformed into z-scores. After the transformation, what are the values for the mean and standard deviation for the sample of z-scores? Select one: a. M = 85 and s = 12 b. M = 0 and s = 1 c. M = 85 and s = 1 d. M = 0 and s = 12
b. M = 0 and s = 1
10. For a normal population with µ = 40 and σ = 10 which of the following samples has the highest probability of being obtained? Select one: a. M ≤ 44 for a sample of n = 4 b. M ≤ 42 for a sample of n = 4 c. M ≤ 42 for a sample of n = 100 d. M ≤ 44 for a sample of n = 100
b. M ≤ 42 for a sample of n = 4
3. A random sample of n = 4 scores is selected from a population. Which of the following distributions definitely will be normal? a. The distribution of sample means will form a normal distribution. b. Neither the sample, the population, nor the distribution of sample means will definitely be normal. c. The scores in the sample will form a normal distribution. d. The scores in the population will form a normal distribution
b. Neither the sample, the population, nor the distribution of sample means will definitely be normal.
4. For a population of N = 10 scores, you first measure the distance between each score and the mean, then square each distance and find the sum of the squared distances. What value have you calculated? a. none of the other choices is correct b. SS c. the population variance d. the population standard deviation
b. SS SS= Σ(x-µ )^2
Learning Check #1 A sport coach is investigating the impact of a new training method. In words, what would the null hypothesis say? a. The new training program produces different results from the existing one b. The new training program produces results about like the existing one. c. The new training program produces better results than the existing one d. There is no way to predict the results of the new training program
b. The new training program produces results about like the existing one.
8. A researcher administers a treatment to a sample of n = 25 participants and uses a hypothesis test to evaluate the effect of the treatment. The hypothesis test produces a z-score of z = 2.37. Assuming that the researcher is using a two-tailed test, what decision should be made? Select one: a. The researcher should fail to reject H0 with either α = .05 or α = .01. b. The researcher should reject the null hypothesis with α = .05 but not with α = .01. c. Cannot answer without additional information d. The researcher should reject the null hypothesis with either α = .05 or α = .01.
b. The researcher should reject the null hypothesis with α = .05 but not with α = .01.
6. Which combination of factors produces the smallest risk of a Type I error? a. α = .05 with n = 100 and σ = 10 b. The three other options all have the same risk. c. α = .05 with n = 20 and σ = 20 d. α = .05 with n = 20 and σ = 10
b. The three other options all have the same risk
5. The classrooms in the Psychology department are numbered from 100 to 120. A professor records the number of classes held in each room during the fall semester. If these values are presented in a frequency distribution graph, what kind of graph would be appropriate? a. a histogram or a polygon b. a bar graph c. a polygon d. a histogram
b. a bar graph
6. What kind of frequency distribution graph shows the frequencies as bars that are separated by spaces? a. a polygon b. a bar graph c. all of the above d. a histogram
b. a bar graph
1.Which of the following accurately describes a hypothesis test? Select one: a. a descriptive technique that allows researchers to describe a population b. an inferential technique that uses the data from a sample to draw inferences about a population c. a descriptive technique that allows researchers to describe a sample d. an inferential technique that uses information about a population to make predictions about a sample
b. an inferential technique that uses the data from a sample to draw inferences about a population
Learning Check #1 When n is small (less than 30), the t distribution _____. a. is almost identical in shape to the normal z distribution b. is flatter and more spread out than the normal z distribution c. is taller and narrower than the normal z distribution d. cannot be specified, making hypothesis tests impossible
b. is flatter and more spread out than the normal z distribution
Learning Check #3 Which combination of factors is most likely to produce a large value for the F-ratio? a. large mean differences and large sample variances b. large mean differences and small sample variances c. small mean differences and large sample variances d. small mean differences and small sample variances
b. large mean differences and small sample variances
Learning check #5 A distribution of scores shows Mean = 31 and Median = 43. This distribution is probably a. positively skewed b. negatively skewed c. bimodal d. open-ended
b. negatively skewed
7. In a positively skewed distribution, scores with the highest frequencies are _____. a. represented at two distinct peaks b. on the left side of the distribution c. in the middle of the distribution d. on the right side of the distribution
b. on the left side of the distribution
Learning Check #1 A deck of cards contains 12 royalty cards. If you randomly select a card from the deck, what is the probability of obtaining a royalty card? a. p=1/52 b. p=12/52 c. p=3/52 d. p=4/52
b. p=12/52
4. What is measured by the estimated standard error, sM? Select one: a. the average distance between a score and the sample mean b. the average distance between a sample mean and the population mean c. how spread out the scores are in the sample d. how spread out the scores are in the population
b. the average distance between a sample mean and the population mean
1. What term is used to identify the mean of the distribution of sample means? a. the sample mean b. the expected value of M c. the standard error of M d. the central limit mean
b. the expected value of M
9. If a sample of n = 4 scores is obtained from a population with μ = 70 and σ = 12, then what is the z-score corresponding to a sample mean of M = 76? Select one: a. z = 0.50 b. z = 1.00 c. z = 0.25 d. z = 2.00
b. z = 1.00
6. What z-score value separates the top 10% of a normal distribution from the bottom 90%? a. z = -1.28 b. z = 1.28 c. z = -0.25 d. z = 0.25
b. z = 1.28
Learning Check #4 A random sample of n = 16 scores is obtained from a population with µ = 50 and σ = 16. If the sample mean is M = 58, what is the z-score corresponding to the sample mean? a. z=1.00 b. z=2.00 c. z=4.00 d. Cannot determine without more info
b. z=2.00
6. A population with µ = 85 and σ = 12 is transformed into z-scores. After the transformation, what is the standard deviation for the population of z-scores? a. σ = 12 b. σ = 1.00 c. cannot be determined from the information given d. σ = 0
b. σ = 1.00 ***The SD of a set of standardized scores is always 1
8. On an exam with μ = 52, you have a score of X = 56. Which value for the standard deviation would give you the highest position in the class distribution? Select one: a. σ = 4 b. σ = 2 c. cannot determine from the information given d. σ = 8
b. σ = 2
Learning Check #8 A researcher uses a hypothesis test to evaluate H0 µ = 80. Which combination of factors is most likely to result in rejecting the null hypothesis? a. σ = 5 and n = 25 b. σ = 5 and n = 50 c. σ = 10 and n = 25 d. σ = 10 and n = 50
b. σ = 5 and n = 50
Learning Check #7 A study assesses the optimal size (# of other members) for study groups. The variable "Size of group" is a) discrete and interval b) continuous and ordinal c) discrete and ratio d) continuous and interval
c) discrete and ratio
8. After measuring 2 individuals, a researcher can say that Tom's score is 4 points higher that Bill's. The measurements must come from a(n) ________ scale. a) ordinal b) nominal c) interval or ratio d) interval
c) interval or ratio
2. A researcher is curious about the average monthly cell phone bill for high school students in the state of Florida. If the average could be obtained, it would be an example of a ______. a) statistic b) sample c) parameter d) population
c) parameter
5. A vertical line is drawn through a normal distribution at z = 1.20. What proportion of the distribution is on the left-hand side of the line? Select one: a. 0.1151 b. 0.3849 c. 0.8849 d. 0.7698
c. 0.8849
Learning check #3 A Grouped Frequency Distribution table has categories 0-9, 10-19, 20-29, and 30-39. What is the width of the interval 20-29? a. 9 points b. 9.5 points c. 10 points d. 10.5 points
c. 10 points (29.5-19.5= 10)
3. A jar contains 10 red marbles and 30 blue marbles. A random sample of n = 3 marbles is selected from the jar with replacement. If the first two marbles are both blue, what is the probability that the third marble will be red? a. 8/38 b. 10/37 c. 10/40 d. 10/38
c. 10/40
10. The results of a hypothesis test are reported as follows: t(29) = 2.70, p < .05. Based on this report, how many individuals were in the sample? Select one: a. 28 b. cannot be determined from the information provided c. 30 d. 29
c. 30
Learning check #4: For a population with μ = 50 and σ = 10, what is the X value corresponding to z=0.4? a. 50.4 b. 10 c. 54 d. 10.4
c. 54 z= (x-µ)/σ SO x=µ=zσ x=50+ (0.4)(10) x=54
Learning check #4 A sample of four scores has SS = 24. What is the variance? a. 6 b. 7 c. 8 d. 12
c. 8
5. 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? a. 6 b. 2 c. 80 d. cannot be determined without additional information
c. 80
9. As sample size increases _______. Select one: a. the value of df also increases b. the critical values of t move closer to zero. c. All of the other options are true as sample size increases. d. the t distribution becomes more like a normal distribution
c. All of the other options are true as sample size increases.
8. Which of the following is true for most distributions? a. Around 70% of the scores will be located within one standard deviation of the mean. b. Around 50% of the scores will be located within one standard deviation of the mean. c. Around 30% of the scores will be located within one standard deviation of the mean. d. Around 90% of the scores will be located within one standard deviation of the mean
c. Around 30% of the scores will be located within one standard deviation of the mean.
Learning check #3 The standard deviation measures.... a. sum of squared deviation scores b. standard distance of a score from the mean c. Average deviation of a score from the mean d. Average squared distance of a score from the mean
c. Average deviation of a score from the mean
7. What happens to the expected value of M as sample size increases? Select one: a. It decreases b. It also increases c. It stays constant
c. It stays constant
1. Which of the following accurately describes an independent-measures study? Select one: a. It uses one group of participants to evaluate a hypothesis about one population mean. b. It uses the same group of participants in all of the treatment conditions being compared c. It uses a different group of participants for each of the treatment conditions being compared d. none of the other alternatives is correct
c. It uses a different group of participants for each of the treatment conditions being compared
6. A sample of n = 25 individuals is selected from a population with μ = 80, and a treatment is administered to the sample. Which set of sample characteristics is most likely to lead to a decision that there is a significant treatment effect? Select one: a. M = 85 and large sample variance b. M = 85 and small sample variance c. M = 90 and small sample variance d. M = 90 and large sample variance
c. M = 90 and small sample variance
5. A sample has a mean of M = 72. If one person with a score of X = 58 is removed from the sample, what effect will it have on the sample mean? a. cannot be determined from the information given b. The sample mean will remain the same. c. The sample mean will increase. d. The sample mean will decrease.
c. The sample mean will increase.
In an independent-measures hypothesis test, what must be true if t = 0? Select one: a. None of the other 3 choices is correct b. The two population means must be equal. c. The two sample means must be equal d. The two sample variances must be equal
c. The two sample means must be equal
4. If the following distribution was shown in a histogram, the bar above the 15-19 interval would reach from _____ to _____. a. X = 15.5 to X = 19.5 b. X = 15.0 to X = 19.0 c. X = 14.5 to X = 19.5 d. X = 15.5 to X = 18.5
c. X = 14.5 to X = 19.5
6. A population of N = 10 scores has a mean of μ = 6. After one score is removed, the mean is found to be M = 5. What is the value of the score that was removed? Select one: a. X = 10 b. X = 5 c. X = 15 d. X = 3
c. X = 15
10. 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? a. X = 110 b. X = 50 c. X = 69.6 d. X = 90.4
c. X = 69.6
Learning Check #4 For an independent measures research study, the value of cohen's d of r^2 helps to describe a. the risk of a type I error b. the risk of a type II error c. how much difference there is between the 2 treatments whether the difference between the 2 treatments is likely to have occurred by chance
c. how much difference there is between the 2 treatments whether the difference
For the independent-measures t statistic, what is the effect of increasing the difference between sample means? a. decrease the likelihood of rejecting H0 and increase measures of effect size b. decrease the likelihood of rejecting H0 and decrease measures of effect size c. increase the likelihood of rejecting H0 and increase measures of effect size d. increase the likelihood of rejecting H0 and decrease measures of effect size
c. increase the likelihood of rejecting H0 and increase measures of effect size
4. Which of the following correctly describes the effect of increasing the alpha level (for example from .01 to .05)? a. increase the likelihood of rejecting H0 and decrease the risk of a Type I error b. decrease the likelihood of rejecting H0 and decrease the risk of a Type I error c. increase the likelihood of rejecting H0 and increase the risk of a Type I error d. decrease the likelihood of rejecting H0 and increase the risk of a Type I error
c. increase the likelihood of rejecting H0 and increase the risk of a Type I error
7. A normal distribution has μ = 80 and σ = 10. What is the probability of randomly selecting a score greater than 75 from this distribution? a. p = 0.25 b. p = 0.50 c. p = 0.6915 d. p = 0.3085
c. p = 0.6915
5. By definition, a Type I error is ______. a. rejecting a false H1 b. rejecting a true H1 c. rejecting a true H0 d. rejecting a false H0
c. rejecting a true H0
6. 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. a. larger than b. exactly equal to c. smaller than d. unrelated to
c. smaller than
8. What t values form the boundaries of the critical region for a two-tailed test using a sample of n = 9 scores and an alpha level of .05? Select one: a. t = ±2.262 b. t = ±1.833 c. t = ±2.306 d. t = ±1.860
c. t = ±2.306
8. In a normal shaped distribution, ______. a. the scores pile up on the left-hand side and taper off to the right. b. the scores pile up on the right-hand side and taper off to the left. c. the scores pile up in the middle and taper off symmetrically to both sides. d. the scores are evenly distributed across the entire scale of measurement.
c. the scores pile up in the middle and taper off symmetrically to both sides.
2. Which of the following z-score values represents the location closest to the mean? a. z = -1.00 b. z = +1.00 c. z = +0.50 d. z = -2.00
c. z = +0.50
Learning check #7 A population has a μ = 6 and σ = 2. What is the shape of the resulting distribution? a. μ = 60 and σ = 2 b. μ = 6 and σ = 20 c. μ = 60 and σ = 20 d. μ = 6 and σ = 5
c. μ = 60 and σ = 20
Learning Check #1 A researcher is interested in the effect of amount of sleep on high school students' exam scores. A group of 75 high school boys agree to participate in the study. The boys are ..... a) a statistic b) a variable c) a parameter d) a sample
d) a sample
5. Real limits are important whenever you are measuring a(n) ________ variable. a) discrete b) dependent c) independent d) continuous
d) continuous
Learning check #4 Researchers observed the students exam scores were higher the more sleep they had the night before. This study is... a) descriptive b) experimental comparison of groups c) non-experimental group comparison d) correlational
d) correlational
6. An operational definition defines a hypothetical construct ______. a) abstractly, like a construct b) all of the above c) conceptually, like a dictionary definition d) in terms of methods used to measure a manipulate it
d) in terms of methods used to measure a manipulate it
4. The average verbal SAT score for the entire class of entering freshmen is 530. However, if you select a sample of 20 freshman and compute their average verbal SAT score you probably will not get exactly 530. What statistical concept is used to explain the natural difference that exists between a sample mean and the corresponding population mean. a) statistical error b) parametric error c) inferential error d) sampling error
d) sampling error
1. For a population with µ = 40 and σ = 8, what is the z‑score corresponding to X = 46? a. +1.00 b. +1.50 c. +0.50 d. +0.75
d. +0.75 z= (x-µ)/σ z= (46-40)/8 z=6/8 z=0.75
2. 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 randomly selected morning, what is the probability that John's drive to work will take between 36 and 40 minutes? a. 0.0793 b. 0.1554 c. 0.1526 d. 0.3108
d. 0.3108
3. What is the value of SS (sum of squared deviations) for the following sample? Sample: 2, 3, 4, 7 a. 78 Incorrect b. 14/3 = 2.67 c. 72 d. 14
d. 14
4. Samples of size n = 4 are selected from a population with μ = 80 with σ = 8. What is the standard error for the distribution of sample means? a. 2 b. 8 c. 80 d. 4
d. 4
8. What is the median for the following set of scores? Scores: 1, 2, 6, 11, 17 a. 8.5 b. 8 c. 4 d. 6
d. 6
1. What is the mean for the following scores? Scores: 1, 6, 14 a. 10.5 b. 3 c. 6 d. 7
d. 7
2. Samples of size n=4 are selected from a population with μ = 80 with σ = 8. What is the expected value for the distribution of sample means? a. 40 b. 8 c. 20 d. 80
d. 80
Learning check #1 A sample of n = 12 scores has a mean of M = 8. What is the value of ΣX for this sample? a. 1.5 b. 4 c. 20 d. 96
d. 96
1. Which of the following is a fundamental difference between the t statistic and a z-score? a. The t statistic computes the standard error by dividing the standard deviation by n - 1 instead of dividing by n b. The t statistic uses the sample mean in place of the population mean c. All of the above are differences between t and z. d. The t statistic uses the sample variance in place of the population variance
d. The t statistic uses the sample variance in place of the population variance
2. The alternative hypothesis for an independent-measures t test states ______. Select one: a. There is no mean difference between the two samples being compared. b. There is no mean difference between the two populations being compared c. There is a non-zero mean difference between the two samples being compared d. There is a non-zero mean difference between the two populations being
d. There is a non-zero mean difference between the two populations being compared.
Learning Check #1 Which combination of factors is most likely to produce a significant value for an independent-measures t statistic? a. small mean difference and small sample variance b. large mean difference and large sample variance c. small mean difference and large sample variances d. a large mean difference and small sample variances
d. a large mean difference and small sample variances
9. A researcher administers a treatment to a sample of participants selected from a population with µ = 80. If a hypothesis test is used to evaluate the effect of the treatment, which combination of factors is most likely to result in rejecting the null hypothesis? Select one: a. a sample mean near 80 with α = .01 b. a sample mean much different than 80 with α = .01 c. a sample mean near 80 with α = .05 d. a sample mean much different than 80 with α = .05
d. a sample mean much different than 80 with α = .05
7. What is the consequence of a Type II error? a. concluding that a treatment has no effect when it really does b. concluding that a treatment has an effect when it really does c. concluding that a treatment has no effect when it really has no effect d. concluding that a treatment has an effect when it really has no effect
d. concluding that a treatment has an effect when it really has no effect
10. For a negatively skewed distribution with a mode of X = 25 and a median of 20, the mean is probably _____. a. cannot be determined from the information given b. greater than 25 c. between 20 and 25 d. less than 20
d. less than 20
2. Which of the following accurately describes the critical region? a. outcomes with a very low probability whether or not the null hypothesis is true b. outcomes with a high probability if the null hypothesis is true c. outcomes with a high probability whether or not the null hypothesis is true d. outcomes with a very low probability if the null hypothesis is true
d. outcomes with a very low probability if the null hypothesis is true
Learning Check #4 Find the proportion of the normal curve that corresponds to z > 1.50 a. p= 0.9332 b. p=0.5000 c. p=0.4332 d. p=0.0668
d. p=0.0668
3. The z-score boundaries for the critical region are determined by ______. Select one: a. the null hypothesis b. the size of the standard error c. the sample data d. the alpha level
d. the alpha level
9. The smallest score in a population is X = 5 and the largest score is X = 10. Based on this information, you can conclude that ______. a. None of the other choices is correct. b. the population mean is between 5 and 10, and the standard deviation is less than 6. c. the population standard deviation is smaller than 6. d. the population mean is somewhere between 5 and 10.
d. the population mean is somewhere between 5 and 10.
10. Which of the following is an accurate definition for the power of a statistical test? Select one: a. the probability of rejecting a true null hypothesis b. the probability of supporting true null hypothesis c. the probability of supporting a false null hypothesis d. the probability of rejecting a false null hypothesis
d. the probability of rejecting a false null hypothesis
10. For a particular sample, the largest distance (deviation) between a score and the mean is 11 points. The smallest distance between a score and the mean is 4 points. Therefore, the standard deviation _____. a. It is impossible to say anything about the standard deviation. b. will be greater than 11 c. will be between 4 and 11 d. will be less than 4
d. will be less than 4
The z test is used to ....
determine the effect of an independent variable on a dependent variable by comparing a sample mean to the mean of an unknown population using the z-statistic
the t test for independent groups designs is used to ....
determine the effects of an independent variable on a dependent variable by comparing the means to 2 independent samples
formula to find z
z= (x-µ)/σ SO x=µ=zσ (x-µ)= deviation score σ = expresses deviation in standard deviation units