PSYCH STATS EXAM 3
Probability values can range from _________ to ________. a. .0000 - 1.0000 b. -1.0000 - 1.0000 c. -0.5000 - 0.5000 d. There are no limits to the range of probability values.
a. .0000 - 1.0000
If a set of events are mutually exclusive and exhaustive, the sum of their individual probabilities equals a. 1 b. 0 c. 1/2 d. Need more information to determine sum
a. 1
z-test statistic
a value that is computed using sample data that us used to determine the p-value associated with the test
The spread of the sample mean decreases when
the sample size is increases.
Critical Value
a z-score that is found by shading the rejection region specified by the level of significance
k
# of groups
Degrees of freedom (df) for one sample t-test
(n-1)
A normally distributed continuous variable has a population mean of 60 and a standard deviation of 14. If one draws a score from the distribution, what is the probability that it will be between 38 and 60?
0.4418
A normally distributed continuous variable has a population mean of 60 and a standard deviation of 14. If one draws a score from the distribution, what is the probability that it will be less than 60?
0.500
A normally distributed continuous variable has a population mean of 60 and a standard deviation of 14. If one draws a score from the distribution, what is the probability that it will be greater than 40?
0.9236
Steps for hypothesis testing
1) state hypothesis 2) set the criteria for a decision 3) collect data and compute sample statistics 4) make a decision
General Notations
All Chapters
Chapter 17
Anova Notations/Vocabulary
Assumptions for independent measures t-test
Assumption of homogeneity of the variance. We have to have equal variances because we are comparing two populations.
Assumptions of one sample t-test
Assumption of normality. The assumption that everyone was distributed normally. Don't question assumption unless sample is very small.
Assumptions for repeated measures t-test
Assumption of normality. The assumption that the population of all the different scores is normally distributed.
Homework 9, Chapter 15 & 17
Chi-Square Test AND Anova Tests
Degrees of freedom (df) repeated measures t-test
Df = (n-1)
How do you write things in APA style?
Example: yes, there is a significant difference in... t(df)=t value, p < .05
A t curve is bell-shaped like the z curve but is less spread out.
False
For a sample size n, there are n - 1 degrees of freedom associated with the goodness-of-fit test statistic, X^2.
False
If the null hypothesis is not rejected, there is strong statistical evidence that the null hypothesis is true.
False
The P-value for a hypothesis test concerning the difference in two population proportions is always calculated by finding the area to the right of the test statistic, regardless of the alternative hypothesis.
False
The large sample z test for mu1 - mu2 can be used as long as at least one of the two sample sizes, n1 and n2, is greater than or equal to 30.
False
The number of degrees of freedom of the two-sample t test are the same as the degrees of freedom for the paired t test statistic.
False
The power of a test is the probability of failing to reject the null hypothesis.
False
The statistical methods of analysis of an variance assume equal sample means in the null hypothesis
False
α is called the observed significance level.
False (P-Value is OBSERVED significance level)
How do you know when to use greater or less than in APA style?
If you reject, you use less than. P < .05 If you fail to reject, you use greater than. P > .05
Repeated measures t-test
It is the experiment where there is one sample being tested twice.
Remember df= (n-1), if we are tying to find n, ( one sample t-test or repeated measures t-test).
Just add df by 1. To find what n is.
Remember df= (n-1), if we are trying to find n, ( independent measured t-test)
Just add df by 2. To find what n is. You add by two because there are two groups, and you subtracted 1 from each df when you combined the df.
Homework 6, Chapter 12
One Sample Hypotheses Test for Population Mean
Homework 5: Chapter 10
One Sample Hypotheses Test for Population Proportion
Summary of all t-test and how to differentiate.
One sample t-test: population mean information in the problem. Independent measures t-test: two separate groups in the problem. Repeated measured t-test: one sample being measured twice in the problem.
Chapter 10 & 12
One-Sample Hypothesis Testing Vocabulary
When do you combine degrees of freedom?
Only for independent measured t-test
Conduct hypothesis test with independent measures t-test
T= (M1-M2)/s(m1-m2) Both groups means subtracted then divided by the estimated standard error. We ignore the population mean part of the t test formula because we don't know that information (:
Conduct hypothesis test with one sample t-test
T= M-μ/ sm
Conduct hypothesis test with repeated measures t-test
T= MD/ SMD We ignore the population mean because we do not have that information.
Decision
Reject Ho OR Fail to reject Ho
Estimated standard error for repeated measures t-test
SMD = √s²/n or SMD= s/√n Remember s² is variance Remember s is standard deviation Whatever information given to you, you could use either formulas.
Estimated standard error for one sample t-test
Sm= s/√n or Sm= √s²/n Remember s is standard deviation. Remember s² is variance. Whatever information is given to you, you could use either formula.
S²
Symbol for sample variance
S
Symbol for standard deviation
A new type of gasoline additive has the potential to revolutionize the fuel industry as we know it. The gas companies have made numerous measurements of fuel efficiency, and have found a mean of 24.7 mpg and a SD of 4.8. To test the new additive, a sample of 75 cars are tested using the new additive. The tests find a mean of 26.5 mpg. What is the null hypothesis?
The new additive will not significantly increase mpg.
A new type of gasoline additive has the potential to revolutionize the fuel industry as we know it. The gas companies have made numerous measurements of fuel efficiency, and have found a mean of 24.7 mpg and a SD of 4.8. To test the new additive, a sample of 75 cars are tested using the new additive. The tests find a mean of 26.5 mpg. What is the directional hypothesis?
The new additive will significantly increase mpg.
Degrees of freedom (df) for independent measures t-test
There will be two groups; hence two separate values of n. You must combine the degrees of freedom for independent measures t-test.
(x bar, subscript 1, minus x bar subscript 2) is an unbiased statistic that is used to estimate mu1 - mu2.
True
A type II error is made by failing to reject a false null hypothesis.
True
An analysis of variance may be used to test the differences in the means of more than two independent populations.
True
As n grows larger, the mean of the sampling distribution of (x bar) gets closer to the population mean.
True
Determining the table value for the F distribution requires two values for degrees of freedom.
True
For n sufficiently large, the distribution of (x bar minus mu, subscript x bar, over sigma subscript x bar) is approximately a standard normal distribution.
True
It is customary to say that the result of a hypothesis test is statistically significant when the P-value is smaller than α.
True
Small P-values indicate that the observed sample is inconsistent with the null hypothesis.
True
The chi-squared test statistic, x^2, measures the extent to which the observed cell count differ from those expected H subscript zero, is true.
True
The hypothesis (P1=P2) is equivalent to the hypothesis (P1-P2=0).
True
The level of significance of a test is the probability of making a type I error, given that the null hypothesis is true
True
The statistical methods of analysis of variance assume that the populations are normally distributed.
True
Two samples are said to be independent when the selection of the individuals in one sample has no bearing on the selection of those in the other sample.
True
Homework 8, Chapter 13
Two Sample Hypotheses Test for Population Mean AND Matched Pairs Test
Homework 7, Chapter 11
Two Sample Hypotheses Test for Population Proportion
Sample standard deviation formula
Used for one sample t test S= √SS/ (n-1) or √SS/df
Sample variance formula
Used for one sample t test S²= SS/(n-1) or SS/df
When do you use the independent measures t-test formula?
When the problem has two study groups. For example: women and men. Or experiment group and control group. Need pooled variance to estimate the standard error.
When do you use the repeated measures t-test formula?
When the problem uses keywords like: again, or day 1 and day 2. The problem must imply that it is one group of people that is being tested twice.
When do you use the one sample t-test formula?
Whenever you see anything representing the population or population mean. That is how you know it is a one sample t-test.
One sample t-test
You can tell it is a one sample t-test because it is the only one with population mean.
Independent measures test
You can tell this is an independent measures t test because it would be the only that has two separate groups.
How and with what information do you use to find the critical values in the t-table?
You need degrees of freedom, alpha level, and whether it is a one-tailed or two-tailed test.
Estimated standard error for independent measures t-test
You need to find pooled variance first before finding estimated standard error. Pooled variance=s²p= SS1+SS2/df1+df2 ( sum of squares from both groups added then divided by combined degrees of freedom from both groups). Estimated standard error s(m1-m2)= √s²p/n1 + s²p/n2 (Pooled variance divided by first group n , then added to the pooled variance divided by second group n, then square rooted). Remember to follow order of operations. Pooled variance you add sums of squares and degrees of freedom first. Then you divide. Estimated standard error you divide first then add, then square root.
Null hypothesis (Ho)
a claim about the population characteristics that is initially assumed to be true
Hypotheses (Ho & Ha)
a statement/question about the population characteristic
Which is true of the sampling distribution of a statistic? a. It gives all the values that a statistic can take b. It gives the probability of getting each value under the assumption that it results due to the independent variable c. Sampling distributions are the same regardless of sample size d. Binomial distributions are never an example of a sampling distribution
a. It gives all the values that a statistic can take
For samples of any size N, the sampling distribution of the mean a. has a mean equal to the mean of the raw score population b. is made up of population mean scores c. has a standard deviation equal to the standard deviation of the raw score population d. all of the above
a. has a mean equal to the mean of the raw score population
A directional hypothesis is to a ______________ as a non-directional hypothesis is to a __________. a. one-tailed test, two-tailed test b. experimental design, repeated measures design c. two-tailed test, one-tailed test d. null hypothesis, alternative hypothesis
a. one-tailed test, two-tailed test
The probability of the combination of two independent events (A and B) occurring is a. p(A) x p(B) b. p(A) - p(B) c. p(A) / p(B) d. p(A) + p(B)
a. p(A) x p(B)
If alpha equals 0.05 and the probability level of your experiment is 0.04, you would _________. a. reject the null hypothesis b. retain the null hypothesis c. accept the null hypothesis d. redo the experiment
a. reject the null hypothesis
Drawing a card from a deck, NOT putting that card back into the deck, then drawing another card is an example of a. sampling without replacement b. sampling with replacement c. linear sampling d. poor sampling procedure
a. sampling without replacement
If N decreases from 50 to 6, the sampling distribution of the mean a. will less likely be a normal distribution b. will always be a normal distribution c. will always be negatively skewed d. will never change
a. will less likely be a normal distribution
Suppose you have a deck of cards: 2 blue stars, 3 red stars, 4 blue circles, 7 red circles, 1 blue square, 4 red squares, 6 blue triangles, and 3 red triangles. What is the probability of (assume mutually exclusive events with sampling with replacement) Obtaining a blue star or a red circle in one draw?
addition rule 2/30 + 7/30 = 0.3
The researcher completed her study with one individual (had one score, transformed into a z score) and found an obtained probability of 0.03. Assuming alpha = 0.05, what should her conclusion be? a. Retain the null hypothesis b. Reject the null hypothesis c. The results are unimportant d. There is not enough information to reach a conclusion
b. Reject the null hypothesis
For which situation would only the multiplication rule be used? a. The probability of tossing at least 2 heads in three coin tosses b. The probability of drawing 3 aces in a row from a deck of cards with replacement c. The probability of drawing a king from a deck of cards d. The probability of getting a sum of 8 in a roll of dice
b. The probability of drawing 3 aces in a row from a deck of cards with replacement
Rejecting H0 when H0 is true is an example of a a. correct decision b. Type I error c. Type II error d. Type III error
b. Type I error
Under what circumstance(s) is it not appropriate to use a directional hypothesis? a. When past research suggests it is appropriate b. When you didn't find significant results with a non-directional hypothesis. c. When the decision is based on theoretical reasoning. d. It is never appropriate to use a directional hypothesis.
b. When you didn't find significant results with a non-directional hypothesis.
Alpha level determines a. sample size b. critical region of rejection of the null hypothesis c. population standard deviation d. all of the above
b. critical region of rejection of the null hypothesis
A researcher is studying the effects of sleep deprivation on irritability. Stating that sleep deprivation will have no effect on level of irritability is an example of a(n) a. correct statement b. null hypothesis c. alternative hypothesis d. Type I error
b. null hypothesis
A researcher's zobt is 1.85 and his zcrit is 2.33. The researcher should a. reject the null hypothesis b. retain the null hypothesis c. retain the alternative hypothesis d. accept the alternative hypothesis
b. retain the null hypothesis
If a researcher is able to reject the null hypothesis, he can say his results are a. correct b. significant c. important d. more than one of the above
b. significant
Which of these events would have a probability of 0.2500? a. Rolling a 4 in one roll of a die b. Getting Heads in one toss of a coin c. Drawing a heart from a deck of cards d. Getting 2 heads in three coin tosses
c. Drawing a heart from a deck of cards
A researcher wanted to calculate the probability of rolling a 4 if a die is rolled 50 times. He didn't roll any dice himself. Instead, he calculated the probability based on reason alone. This is an example of what type of probability? a. a posteriori b. algebraic c. a priori d. continuous
c. a priori
A researcher draws all possible samples for various values of N from the same population of raw scores. If N increases, standard error of the mean a. increases b. remains the same c. decreases d. is unable to be calculated
c. decreases
A positively skewed raw score distribution will produce a sampling distribution of the mean for N= 308 that is a. positively skewed b. negatively skewed c. normally distributed d. unable to be determined
c. normally distributed
The null hypothesis which is appropriate for a directional alternative hypothesis asserts that _________. a. the independent variable has had no effect b. chance alone is responsible for the differences between conditions c. the independent variable does not have an effect in the direction predicted by H1 d. b and c
c. the independent variable does not have an effect in the direction predicted by H1
P hat, subscript c
combined sample proportion
The critical value for the z distribution using α = .051 tail (towards the right side of the distribution) a. ± 1.645 b. + 1.96 c. - 1.645 d. + 1.645
d. + 1.645
Which of these situations involves independent events? a. Sampling with replacement b. Sampling without replacement c. The probability associated with coin tosses d. Both a and c
d. Both a and c
What is not true of a random sample? a. each possible sample size has an equal chance of being selected b. all members of a population have an equal chance of being selected c. assures sample is representative of the population d. all above are true
d. all above are true
A random sample a. is representative of the population from which it was drawn. b. ensures that everyone in the population has an equal likelihood of being sampled c. ensures that every possible sample of a particular size has an equal chance of being sampled d. all of the above
d. all of the above
The z test is appropriate when a. the experiment involves a single sample mean b. parameters of the null hypothesis population (mean and standard deviation) are known c. sampling distribution of the mean is normally distributed d. all of the above are correct
d. all of the above are correct
Which of the following is NOT an example of mutually exclusive events? a. being male and being female b. having brown eyes and having blue eyes c. rolling a 3 and rolling a 5 (on a single roll of one die) d. being a student and being an athlete
d. being a student and being an athlete
When evaluating the results of a study, we directly assess the a. experimental theory b. beta level c. alternative hypothesis d. null hypothesis
d. null hypothesis
df, subscript b
degrees of freedom between (k-1)
df, subscript w
degrees of freedom within (N-k)
SSE
error sum of squares
True or False: It is always appropriate to use a directional alternative hypothesis.
false
True or False: We always directly evaluate H1 when analyzing the data.
false
MSE
mean squared error (SSE/N-k)
MSTr
mean sum of squares (SSTr/k-1)
Suppose you have a deck of cards: 2 blue stars, 3 red stars, 4 blue circles, 7 red circles, 1 blue square, 4 red squares, 6 blue triangles, and 3 red triangles. What is the probability of (assume mutually exclusive events with sampling with replacement) A star on the first draw and a circle on the second with replacement?
multiplication rule 5/30 X 11/30 = 0.611
x-double bar
overall mean
N
overall sample size
sigma
population standard deviation
P
proportion (Probability in Chi-Square test)
A new type of gasoline additive has the potential to revolutionize the fuel industry as we know it. The gas companies have made numerous measurements of fuel efficiency, and have found a mean of 24.7 mpg and a SD of 4.8. To test the new additive, a sample of 75 cars are tested using the new additive. The tests find a mean of 26.5 mpg. Using α=0.051 tail what is your conclusion?
reject null
x bar
sample mean
x-bar, subscript i
sample mean of each group i
P hat
sample proportion (number of successes over sample size)
n
sample size
n, subscript i
sample size of each group i
s
sample standard deviation
s, subscript i
sample standard deviation
s^2
sample variance
F
test statistic - F ratio (MSTr/MSE)
Uo (mu)
the hypothesized value, the value you believe is true for the population mean
Po
the hypothesized value, the value you believe is true for the population proportion
Level of significance (alpha)
the probability of a Type I Error
P-Value
the probability of observing values more extreme than the test statistic
Alternative hypothesis
the research question (dictates how to shade the z-curve)
Type II Error
the researcher failed to reject the null hypothesis, but the null hypothesis was false
Type I Error
the researcher rejected the null hypothesis, but the null hypothesis was true
SSTr
treatment sum of squares
True or False: It is permissible to use a directional H1 when there are good theoretical as well as strong supporting data to justify the predicted direction
true
True or False: Regardless of whether H1 is directional or nondirectional, when evaluating H0 we always assume chance is responsible for the differences in results between conditions.
true
True or False: We always evaluate the tail of the distribution, beginning with the obtained result, rather than just the obtained result itself.
true
Mu (u)
true mean
