quizzes stats - all
A stem and leaf plot shows the following key: 7|2 = 720. If a stem in this plot has a value of 8 with a leaf of 3, what number do these values represent?
830
A high school teacher assesses whether class rankings for a math class are related to class rankings in an English class.
Spearman r
If we conduct 4 comparisons (tests) at alpha = 0.05, what is our overall Type I error rate? Make sure to note the alpha! Report 3 decimal places in your answer.
0.185 -- use 1-(1-alpha test)^#tests
Scenario 1: X =20, μ = 10, σ = 5, n = 25, α = 0.01
1a. The approprate test statistic is a ______ and the symbol for the effect size is ______. one-sample z test; d -- d=xbar-meanxbar/sdx --pop sd is known 1b. What is the value of the effect size? 2 -- 20-10/5
Scenario 2: X = 19, μ = 13, s = 6, n = 16, α = 0.01
2a. The approprate test statistic is a ______ and the symbol for the effect size is ______. one-sample t test; g -- g=xbar-meanx/sx --sx est. pop sd -pop sd is unknown 2b. What is the value of the effect size? 1
A ________________ variable classifies individuals based on some attribute or characteristic.
A qualitative variable classifies individuals based on some attribute or characteristic.
A _________________ is a numerical measurement describing some characteristic of a sample
A statistic is a numerical measurement describing some characteristic of a sample.
A researcher measures the resting heart rate of a group of 25 patients before and afterthey take a particulardrug.
A t test for dependent means should be used, because the two sets of scores are from a single group of people.
There is some concern that if a woman has an epidural to reduce pain during childbirth, the drug can get into the baby's bloodstream, making the baby sleepier and less willing to breastfeed. A Journal published results of a study conducted at a university. Researchers followed up on 1184 births, noting whether the mother had an epidural and whether the baby was still nursing after 6 months. The results are shown to the right.
A chi-square test for independence These data differ from other kinds of data because they categorize subjects from a single group on two categorical variables rather than on only one. A chi-square test for independence is used here. State the null and alternative hypotheses. H0: Breastfeeding sucess is independent of having an epidural.Ha:There's an association between breastfeeding success and having an epidural.
Movies are classified as either violent or not violent; they are also classified as either containing "adult themes" or not containing "adult themes." A researcher wonders whether violence and "adult themes" in movies are related.
Chi square independence
A professor wondered whether grades on her midterm predicted (i.e., were related to) grades on her final. Assume both grades are quantitative/numeric.
Pearson r
Assume the probability that someone has ever owned a pet is 0.9. The following scenario is based on randomly sampling 5 people and asking them about their pet ownership (yes/no).
Complete the table showing the distribution associated with this problem, where x is the number of people who have ever owned a pet. x P(X=x) 0 0 1 0.0004 2 0.0081 3 0.0729 4 0.3281 5 0.5905 SUM 1 --if all 5 have pet (.9)^5 if none have a pet (.1)^5 if one has a pet (.1)(.1)(.1)(.1)(.5) times 5 What's the probability that between two and four people in the sample (inclusive) have ever owned a pet? 0.4091
A known population of midterm exam grades for a biology class has a mean of 82 and a standard deviation of 12.2. A professor wonders if midterm grades after switching to online instruction for this class (Xbar= 79.9) differ from the known midterm grades. What null hypothesis will he test?
H0: μx = 82
A joint probability distribution is shown below. Determine both P(C3|R1) and P(R1|C3).
Identify P(C3|R1). P(C3|R1)=0.245 -- (0.12)/(0.49) Identify P(R1|C3). P(R1|C3)=0.5 -- (0.12)/(0.24)
A data set has the following characteristics: r = 0.4 sx = 2 sy = 3 Xbar = 19 Ybar = 28 n = 10 b0 = 16.6 b1 = .6 eqn: Y'=b1(X) + b0
If X = 15 , what is Y'? Y' = 25.6
Decide whether or not the two events are independent or whether it is not possible to tell. Justify your answer. P(D)=13 and P(C|D)=23
It is not possible to tell if C and D are independent. We need to know either P(C) or P(D|C).
Determine which level of measurement is most appropriate. Base your answer on how the variable is measured, not any underlying property. Favorite team sports (e.g., soccer, basketball, football)
Nominal
Use the following data set to answer the questions below. 1, 3, 4, 5 --IQR = Q3 - Q1
Obtain the quartiles. Q1 = 1.5 Q2 = 3.5 Q3 = 4.5 Determine the interquartile range. The interquartile range is 3.
Suppose that A and B are independent events such that P(A)=0.8 and P(B)=0.7. Find P(A & B).
P(A & B)=0.56 -- (0.8)(0.7)
Suppose that E and F are two events and that P(E & F)=0.1 and P(E)=0.2. What is P(F|E)? --P(F|E)=P(F and E)/p(E)
P(F|E)=0.5
Subjects rate their marital satisfaction and job satisfaction, both measured on a scale of 1 to 100, and a researcher assesses whether these two variables are related to each other.
Pearson or Pearson r
The histogram to the right represents the weights (in pounds) of members of a certain high-school debate team. What is the class width? What are the approximate lower and upper class limits of the first class? -apparent limit: extend from the smallest unit of measure in the interval to the largest -real limit: extend from half of the smallest unit of measure below the score to half above -real limit of an interval: extend from half the measurement limit below the lowest score to half above the highest score: i= upper real limit - lower real limit
The class width is 20. What are the approximate lower and upper class limits of the first class? The approximate lower class limit is 109.5. The approximate upper class limit is 130.5.
The given data represent the number of people from a town, aged 25-64, who subscribe to a certain print magazine. Construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how? Age People 25-34 540 35-44 821 45-54 184 55-64 70
The distribution appears to be skewed to the right (or positively skewed).
A sample of 55 rodent burrows, whose depths were measured in centimetres, yielded the frequency histogram to the right. State whether the distribution is (roughly) symmetric, right skewed, or left skewed.
The distribution is right skewed.
The line that fits best between the points in a scatterplot is the line that gives the _______ sum of the squared _______ distances between each point and the line.
The line that fits best between the points in a scatterplot is the line that gives the smallest sum of the squared vertical distances between each point and the line.
The boxplot shown below results from the heights (cm) of people listed in a data set. What do the numbers in that boxplot tell us?
The maximum height is 195 cm. The minimum height is 151 cm. Q3 is 182.6 cm. The median is 172.8 cm.
In a study of the effects of radiation on amphibian embryos, the time it took a sample of seven different species of frogs' and toads' eggs to hatch was recorded. The following table shows the times to hatch, in days. 5, 9, 14, 5, 4, 4, 14
The mean is 7.8 The median is 5 (middle value, order data) The modes are 4, 5, 14.
If a professor adds 10 points to each student's final exam score, how will it affect the class mean on the final exam?
The mean will increase by 10 points.
Six depression inventory scores are randomly selected from a population of scores. The six depression scores have a mean of 22.167 beats per minute. Five of the six scores are as follows: 6, 16, 7, 32, 35 What's the missing value?
The missing value is 37 (96+x=133.002)
Which normal distribution has a wider spread: the one with mean 2 and standard deviation 1 or the one with mean 1 and standard deviation 2?
The normal distribution with mean 1 and standard deviation 2 has the wider spread because spread is represented by the standard deviation σ and the distribution with the greater standard deviation has the wider spread.
Suppose P(A)=0.9 and P(B|A)=0.1. Find P(A & B).
The probability P(A & B) is 0.09 -- (0.9)(0.1)
For the following data set, what is the range? 5, 4, 1, 7, 8 --range, difference between the lowest and highest scores
The range is 7.
The sums of squares for the data set below is 29.2 4, 6, 1, 8, 3 --sample variance/est of pop variance SSx/n-1 --sample SD/est of pop sd sqroot(SSx/n-1)
The sample variance is 7.3 The sample standard deviation is 2.70
Allie calculated a correlation coefficient of −0.72. She made a mistake in her calculation since the correlation coefficient cannot be negative.
The statement is false.
For each p-value and alpha below, indicate whether you would reject or fail to reject the null hypothesis. a. p=0.772, α = 0.05
The statistical conclusion is: fail to reject the null
For each p-value and alpha below, indicate whether you would reject or fail to reject the null hypothesis. b. p=0.352, α = 0.05
The statistical conclusion is: fail to reject the null
A researcher conducts a dependent samples t-test and obtains the following p-value. What would her statistical decision be, assuming the specified alpha? p=0.234, α = 0.01
The statistical conclusion is: fail to reject the null
The table below displays a set of 20 scores for a multiple choice final exam. 3, 6, 13, 13, 16, 17, 18, 18, 20, 21, 22, 22, 22, 23, 25, 25, 26, 27, 27, 27
The sum of the 20 scores is 391. Thus, the mean is 19.55 To compute the 10% trimmed mean of the data, you need to cut out 22 score(s) from each side of the data set. You would then sum the remaining scores and divide by 16 to get the trimmed mean.
Use the deviation score method (as shown in class) to calculate the sums of squares. 6, 4, 3, 9, 2 --list all X'S, calculate mean (xbar), calculate all deviation scores ((x-xbar)^2), sum all (x-xbar)^2 to get SS
The sums of squares is 30.8
Based on the given information, decide whether or not the two events in question are independent or whether it is not possible to tell. P(C)=0.4, P(D)=0.3, and P(C & D)=0.12
The two events are independent because P(C & D)=P(C)•P(D).
Based on the given information, decide whether or not the two events in question are independent or whether it is not possible to tell. P(B)=0.2 and P(B∣A)= 0.5 --to determine independence: p(A|B) = p(A) p(B|A) = P(B)
The two events are not independent because P(B∣A)≠P(B).
If a student's z-score for an exam is positive 2.1, what must be true?
Their score is 2.1 standard deviations above the mean.
Brenda is a huge sports fan. She wondered if there was a relationship between someone's favorite sport and where they lived. She randomly sampled 500 American sports fans and asked each what their favorite sport was (football, baseball, basketball, soccer, or other) and what part of the country they lived in (Northeast, Southeast, Midwest, Rocky Mountains, Pacific Coast). Assuming all conditions are satisfied, which of the following tests should Brenda use to test her hypothesis?
The chi-square test of independence There was one population and Brett was gathering information on two categorical variables on each person in the sample.
Brenda is a huge sports fan. She hypothesized half of sports fans liked football the best, one-quarter liked baseball the best, 15% liked basketball the best, and 5% liked soccer the best, and the rest liked some other sport the best. She surveyed 100 sports fans and asked what sport they liked the best. Assuming all conditions are satisfied, which of the following tests should Brenda use to test her hypothesis?
The goodness-of-fit chi-square test There is only one population (sports fans) and a categorical variable was examined on this population.
If the area to the left of a z-score is greater than 0.5, what must be true?
The z-score must be positive.
Workers at a grocery store undergo shelf-stocking efficiency training. The store supervisor's satisfactions with shelf stocking on the day of the training and three months after the training are compared.
This scenario should be analyzed using paired data because the groups are dependent and have a natural pairing.
The correlation between variables X and Y in a sample of 35 students is −0.308.
To assess if there is a correlation in the population from which the students were drawn, a researcher would test the following null hypothesis: A. ρ = 0 --correlation for two populations b) Based on α = .01, the critical value is r = +/- 0.43 --use df =n-1 use r table c) Based on the above information, what is your statistical conclusion about the correlation between variables X and Y (α = .01)? fail to reject Ho
The following data represent Grandparent (population 1) and Grandchild (population 2) reaction times in response to a computer-generated stimulus. The grandparent and grandchild in each pair are related to each other.
What analysis is most appropriate for assessing if there was a difference in grandparents' and grandchildren's reaction times? dependent samples t-test Use SPSS to calculate the test statistic. Use population 1 (grandparent)−population 2 (grandchild) as the difference score The observed test statistic's value is 2.223 p = 0.068 -- analyze >compare means > paired-samples t-test --scroll to the side, use t and sig
The graph to the right compares teaching salaries of women and men at private colleges and universities. What impression does the graph create? Does the graph depict the data fairly? If not, construct a graph that depicts the data fairly.
What impression does the graph create? The graph creates the impression that men have salaries that are more than twice the salaries of women Does the graph depict the data fairly? No, because the vertical scale does not start at zero.
The unit of measurement for a data set is 100
What is the lower real limit for a score of 900? 850 What is the upper real limit for that score of 900? 950
Suppose it is known that the general population's average rating of their ability to stay focused on a particular task is 4.76. A random sample of 15 college students rated their own focusing ability for the same task (data shown on the right). At the 5% significance level (2-tailed), do the data provide sufficient evidence to conclude that college students differ from the general population?
What test is most appropriate? one-sample t Use SPSS to answer the following questions. Use the icon in the upper right corner to copy the data into SPSS. Make sure to think through what you're doing when you set up the test! p = 0.01 --analyze >compare means >one sample t> enter mean --use sig (2 tailed) g = 0.775 --use the mean in spss - given mean/st dev. in spss --use abs value Accoring to SPSS, the lower bound of the confidence interval is −1.577
Use this partial SPSS output to answer the following questions:
Which line of data should be used? equal variances not assumed How do you know? 0.004 < .05
Use the below source table to answer the following questions.
a) How many groups are there? 3 b) Assuming equal n's, how many subjects are in each group? 6 c) The APA-style report for this statististic would read: F (2,15) = 1.7, MSE = 165 , p > .05 d) Compute eta-squared and report it to 2 decimal places. 0.18 --eta^2=ssb/sst e) Compute omega-squared and report it to 2 decimal places. 0.07 --omega^2=(k-1)(f-1)/(k-1)(f-1)+nt , where nt is total subjects f) Assume the following means for 2 of the groups: A = 10 B = 12 What is the value of qobt for comparing groups A and B ? 0.381 -- use xbar-ybar/sqrt s^2w/n -- 10 - 12 / sqrt(165/6) -- 165 is mse and 6 is n in each group Conduct a Tukey's test using α = .05. What is the statistical conclusion for comparing group A to group B? A. fail to reject Ho -- use tukey table, k is groups, df is df within g) What is the research conclusion for comparing group A to group B ? There is not enough evidence to suggest a difference in mean scores for groups A and B.
Complete the following sentences. a. A standardized variable always has a mean of _______ and a standard deviation of _______. b. The z-score corresponding to an observed value of a variable tells you _______. c. A positive z-score indicates that the observation is ______ the mean, whereas a negative z-score indicates that the observation is _______ the mean.
a. A standardized variable always has a mean of 0 and a standard deviation of 1. b. The z-score corresponding to an observed value of a variable tells you how far the observation is from the mean in units of standard deviation. c. A positive z-score indicates that the observation is greater than the mean, whereas a negative z-score indicates that the observation is less than the mean.
A sample mean, sample size, and population standard deviation are provided below. Perform the required hypothesis test at the 1% significance level. As always, assume a 2-tailed test. xbar=33, n=28, σ=10, H0: μ=30, Ha: μ≠30
a. What type of test is most appropriate in this situation? Why? one sample z test because the population standard deviation is known b. The absolute value of the calculated test statistic (zobt or tobt) is 1.59 -- use z=xbar-mean/(sd/sqrtN) c. Conclusion: Do not reject the null hypothesis. --since alpha is 1%, use 1.96 Zcrit
Loosely based on the document Smartphone Ownership by the Pew Research Center and the document Current Population Survey by the U.S. Census Bureau, we constructed the following joint probability distribution for educational attainment and smartphone ownership for U.S. adults. A U.S. adult is selected at random.
a. Determine the probability that the person selected owns a smartphone. 0.57 b. Determine the probability that the person selected has graduated high school. 0.311 c. Determine the probability that the person selected owns a smartphone and has graduated high school. 0.144 d. Determine the probability that the person selected owns a smartphone, given that the person has graduated high school. 0.463 -- 0.144/0.311 e. Determine the probability that the person selected has graduated high school, given that the person owns a smartphone. 0.252 -- 0.144/0.571
Assume that a 2-tailed test was conducted but that only one alpha region is shown on the diagram. For further clarification: a refers to the entire purple region, b to the small darker purple region, c to the yellow region, and d to the orange striped region.
a. If μ0 = 40 (this is important), which area represents α/2 ? c b. Based on the diagram, in reality, is the null hypothesis true or false? false, because the curves are not overlapping
The data shown to the right represent the number of negative thoughts participants reported during one day. Sample 1 is the control group Sample 2 is treatment group 1 Sample 3 is treatment group 2 Enter the data into SPSS. Are there differences between the 3 groups on number of daily negative thoughts reported?
a. Let μ1, μ2, and μ3 be the population means of samples 1, 2, and 3, respectively. What are the correct hypotheses for a one-way ANOVA test? H0: μ1=μ2=μ3 Ha: Not all the means are equal. What is the outcome variable? number of negative thoughts per day c. According to the SPSS output, Fobt = 1.68 --make groups and put all numbers in one column, analyze >compare means > oneway anova > post hoc > tukey > options > descriptive and means plot d. p=0.254 e. What is your statistical conclusion at α = .05? do not reject H0.
A researcher conducts a two-tailed z-test with μA=2.2, XbarB= −2, zobt = −3, α=0.01.
a. The correct research conclusion would read: Evidence suggests that Group A (μA=2.2) had a higher mean than Group B (XB=−2) on the outcome variable. b. If N = 12, what is the correct APA style report of the z-statistic? z (N=12)= −3, p < 0.01. --use actual n
A researcher conducts a one sample t-test with μA=18.3 and XbarB= 19.9 (N = 6). She finds tobt = 1.12 and uses α= 0.01, two-tailed.
a. The correct research conclusion wouldread:There's not enough evidence to suggest that Group A (μA=18.3) and Group B (XbarB=19.9) differed on the outcome variable. If N = 6, what is the correct APA style report of the t-statistic? t (5) = 1.12, p > 0.01. --use df=n-1
A confidence interval for a population mean has a margin of error of 3.5. a. Determine the length of the confidence interval. b. If the sample mean is 51.7, obtain the confidence interval. c. Construct a graph that illustrates your results.
a. The length of the confidence interval is 7 b. The confidence interval for μ is from 48.2 to 55.2
Use the following summary statistics to answer the questions below Xbar = 11, μ= 5, σ = 5, n = 25, α = 0.01
a. The lower bound of the corresponding confidence interval is 8.425 b. The upper bound is 13.575 -- use zcrit 2.575, (xbar+/-(zcrit)(sdxbar) --sdxbar is sd/sqrt(n) c. Compared to the interval you just computed, if we computed a 95% confidence interval, this new interval would be: morenarrow
Given below is a linear equation. y=1.5x−6 a. Find the y-intercept and slope. b. Determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation. c. Use two points to graph the equation.
a. The y-intercept is −6 and the slope is 1.5 b. The line slopes upward, because the slope is positive.
The following are data on age (in weeks) and crown-rump length (in millimeters) for fetuses. A scatterplot of the data is given to the right. Age (x) 11 12 12 14 18 19 20 22 25 27 Length (y) 64 66 107 105 161 166 179 226 233 279
a. Use SPSS to calculate the correlation coefficient. r 0.984 b. Use SPSS to calculate the slope. = 12.722 --correlation (analyze >correlate >bivariate) --scatterplots (graphs > chart builder > scatter/dot > bottom row add fit at line total)
Answer the qustion about the following data set: X 2 3 4 5 6 Y 4 7 9 8 12 The regression equation for these data is: Y' = 1.7X + 1.2 --e= Y - Yhat (also y prime) 1.7(2)+1.2 = 4.6 4 - 4.6 = -0.6
a. What is e (the residual) for an X of 2? Make sure the sign is correct. -0.6 b. What would the sum of all the e's for this data set be? 0
A 95% confidence interval ranges from 5 to 17.8.
a. What is the mean of the CI? 11.4 b. If the known population mean is 14.7, what would your statistical conclusion be? fail to reject the null
A population has a mean of μ=76 and a standard deviation of σ=27. We take samples of size 81 from the population.
a. What is the shape of the sampling distribution? normal b. What is μxbar? 76 c.What is σxbar? 3 -- 27/sqrt81 d. In answering part (a), what assumptions did you make about the distribution of the variable? No assumptions were made because, for a relatively large sample size, the sampling distribution is normal, regardless of the distribution of the variable under consideration. e. Can you answer part (a) if the sample size is 20 instead of 81? Why or why not? No, because the sample size needs to be at least 30 if the distribution of the variable is unknown.
Use the following information to answer questions about the data shown to the right: Xbar = 2.4 Ybar = 1.8 sx = 2.302 sy = 3.493 SCP = 29.4 x 3 6 2 1 0 y 5 6 0 0 −2 --n = # of pairs --covariance = sum(x-xbar)(y-ybar)/n-1
a. What is n? n = 5 b.What is the covariance? cov = 7.35 c. What is r? r = . 914
Suppose it is known that the average amount of screen time people have per day is normally distributed with a mean of 3.36 hours. A random sample of 15 Portland residents reported their daily screen time (data provided). Use SPSS to conduct the analysis of whether Portland residents differ from the general population on screen time. -- analyze >compare means >one sample t-test> enter mean in test value > ok
a. sXbar = 0.327 --st error mean b. tobt = +/- 3.286
Calculate the two-tailed p-value for each of the following calculated one-sample z values.
a. z=−2.06. The p-value is 0.039 b. z=2.97. The p-value is 0.003 --use z table, small part multiply by 2 for 2 tailed
x 3 6 1 1 0 y 6 7 1 -1 -3
a. Σ(X−X) = 0 b. What is the sum of cross products? SCP =38 --scp is the sum of (x-xbar)for each score multiplied by (y-ybar) for each score
Provided below are summary statistics for independent samples from two populations. Conduct the required hypothesis test (2-tailed) and obtain the specified confidence interval. xbar1=13, s1=2.5, n1=10, xbar2=15, s2=2.4, n2=10
a. First, what are the correct hypotheses for a two-tailed test? H0:μ1=μ2 Ha:μ1≠μ2 b. Next, compute the test statistic. You must show your work, including the equations. spooled = 2.4505 sxbar−ybar = 1.0959 tobt= −1.825 --use sqroot(dfx s^2x=dfy s^2y/ dfx +dfy --use sxbar-ybar=Sp sqroot(1/nx + 1/ny) -- use t = xbar-ybar / sxbar-ybar c. Now determine the critical values for α = 0.05 using the table provided in class. tcrit=±2.101 --use df = n-2, look up in t table d.What is the conclusion of the hypothesis test? (graded based on answers to b and c; you will not receive credit if part b and/or c is missing. do not reject H0. e. The 95% confidence interval ranges from −4.302 to .302. Enter the lower value first! -- use (xbar - ybar) +/- tcrit (sxbar - ybar) f. What is the value of the effect size? g = −0.816 --use xbar - ybar/Sp
A oneway ANOVA compares 4 groups, with 8 subjects in each group.
a. What's df-between? 3 -- k-1 , k is number of groups b. What's df-within? 28 -- nt-k , nt is total n of subjects and k is number of groups
Assume that an exam is normally distributed with μ=73.0 and σ=12.5. --draw out distribtutions
a. What's the probability any one student's exam score will be more than 79? The probability is 0.3156 --calculate Z score (z=xbar-mean/sd), then look up in z-table b. If 16 students are randomly selected, find the probability that they have a mean exam score greater than 79. The probability is 0.0274 --use st error=sd/sqrt(n) , then use z=xbar-mean/xbar(the previous number) , then look up in table c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30? Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.
A data set has the following characteristics: r = 0.5 sx = 9 sy = 3 Xbar = 19 Ybar = 23 n = 6 --slope (method 1) b1=r(Sy/Sx) (method 2) b=covxc/s^2x --intercept b0=Ybar - b1(Xbar) also, Ybar=b1(xbar)+b0 --se = sy*sqroot((1-r^2)(n-1/n-2)) or sqroot(sum(y-ybar)^2/n-2)
a. What's the value of the slope? 0.167 b. What's the value of the intercept? 19.827 c. What's the value of se? 2.905
Researchers determine whether they'll conduct independent or dependent samples tests ______________ collecting their data.
before
A researcher randomly sampled 50 mothers of kids younger than 6 and classified them as being employed full-time outside the home (n=15), employed part-time outside the home (n=10), or not employed outside the home (n=25). She evaluated whether mothers have different employment patterns than women in the general US population in which 50% are employed full-time, 10% are employed part-time, and 40% are not employed
chi-square GOF
. Twenty women rate their level of depression. After participating in a two-month long treatment program, the same women rate their depression levels again. A researcher wonders whether there has been a change in depression level.
dependent t
If they suspect their data will be highly correlated when using paired data, it's recommended that they use a(n) _____________ design because this _______________ variability and _____________ power.
dependent; decreases; increases
If the absolute value of the correlation coefficient (|r|) goes down, the average size of the residuals (e's)
goes up
Do people walk faster in an airport when they are departing (getting on a plane) or after they have arrived (getting off a plane)? An interested passenger watched a random sample of people departing and a random sample of people arriving and measured the walking speed (in feet per minute) of each. Which of the following tests is the most appropriate to use to determine if the mean walking speed is different between departing and arriving passengers at an airport (assuming all conditions for inference are satisfied)?
independent samples t-test
In a television advertisement, a company called "Waist Away" claimed the workout program on their set of DVDs would help people lose weight more than any other DVD workout program. To test this claim, an independent company, called "Slim Down," selected one other DVD program. Then they randomly assigned half the volunteers to the Waist Away program and the other half to the Slim Down program. Each participant was weighed before they started the program and then regularly participated in their assigned program for one month. After one month, each participant was weighed again. The amount of weight lost was recorded for each person, where negative values indicated a weight gain. The average weight loss of the 20 volunteers on the Waist Away program was 3.1 pounds with a standard deviation of 4 pounds, while the average weight loss for the 21 volunteers on the Slim Down program was 2.2 pounds with a standard deviation of 2.3 pounds. Which of the following tests is most appropriate to use to determine if the company's claim is valid?
independent samples t-test
People are randomly assigned to either a control (no training) or training group. A researcher asks whether the two groups differ in reaction times in response to the presentation of a stimulus.
independent t
Is it a good idea to listen to music when studying for a test? A study was performed in which students were randomly assigned to either listen to Mozart or no music while attempting to memorize objects pictured on a page. They were then asked to list all the objects they could remember. Which of the following tests is the most appropriate to use to determine if there is a difference in the mean number of objects remembered between those who listen to Mozart and those who listened to no music while attempting to memorize objects pictured on a page (assuming all conditions for inference are satisfied)?
independent t-test A two-sample t-test is appropriate when the variable of interest is quantitative, there are two populations (or two groups being compared), and the population standard deviations are not known.
According to Cohen's guidelines, how big is the reported effect size? If g = 0.93, the effect size is considered:
large
Do people walk faster in an airport when they are departing (getting on a plane) or after they have arrived (getting off a plane)? An interested passenger watched a random sample of people departing and a random sample of people arriving and measured the walking speed (in feet per minute) of each. What type of study design is being performed?
observational study
Are women getting taller? A researcher claims that the average height of a woman aged 20 years or older is greater than the 1994 mean height of 63.7 inches. She obtains a random sample of 45 women aged 20 years or older and finds the sample mean to be 63.9 inches. Assume the population standard deviation is 3.5 inches. Which of the following tests is the most appropriate to use to test the researcher's claim (assuming all conditions for inference are satisfied)?
one-sample z-test A one-sample z-test is appropriate when the variable of interest is quantitative, there is one population, and the population standard deviation is known or assumed to be known.
A researcher examined whether four state public schools in a particular state differed on average GRE score.
oneway ANOVA
New employees for a large company are randomly assigned to one of three training conditions. The human resources head compares the three groups on mean level of on-the-job efficiency
oneway ANOVA
Many people believe that students gain weight as freshmen in college. To determine if this is true, a student randomly sampled 100 freshmen. Each was weighed when college started in the fall and again when they left for home after the spring term. Should a paired t-test or a two-sample t-test be used to determine if students weigh more at the end of their freshman year compared to the beginning of their freshman year, on average?
paired t-test
In 1993, the British Medical Journal published an article titled, "Is Friday the 13th Bad for Your Health?" Researchers in Britain examined how Friday the 13th affects human behavior. One question was whether people tend to stay at home more on Friday the 13th. The accompanying data give the number of cars passing Junctions 9 and 10 on the M25 motorway for consecutive Fridays (the 6th and 13th) for five different time periods. Assuming all conditions for inference are met, which test is appropriate to use to answer the researcher's question of interest?
paired t-test Since the consecutive Fridays are naturally paired, the paired t-test is appropriate to use.
Determine which level of measurement is most appropriate. Base your answer on how the variable is measured, not any underlying property. gallons of water in a swimming pool
ratio
A researcher assesses whether children's scores on a prejudice and discrimination measure (Likert scale) vary depending on school student body racial composition (primarily white, primarily non-white, or mixed) and level of cultural competency training of staff (trained, not trained).
two way ANOVA (factorial or 2x3 , 3x2)
Children are randomly assigned to watch no TV, 2 hours of network TV, or 2 hours of public TV (e.g., PBS) per day during a 3-week period. A researcher assesses whether TV-watching condition and child grade (2nd, 4th, or 6th) predict the number of prosocial acts observed during 30 min of playground play.
two way ANOVA (factorial or 3x3)
A hospital administrator wondered whether duration of a particular illness was predicted by treatment location (inpatient or outpatient) and treatment type (A, B, C).
twoway ANOVA
A correlation coefficient for a data set is 0.79. The original X values of the data set ranged from 60 to 110. If a data analyst decided to look just at the data where the X's ranged from 75 to 95, the new correlation coefficient for the limited data set
would most likely go down
A correlation coefficient for a data set is 0.5. If someone multiplied each Y score by 10 , the correlation coefficient:
would stay the same
What is the symbol used to represent the population standard deviation?
σ
What is the symbol for standard deviation, as used in the one-sample z-test?
σx
All else being the same, how does each of the following affect the power of a planned study?
(a) Using a smaller α ______ power. decreases (b) A larger predicted difference between the means of the populations _____ power. increases (c) A smaller population standard deviation _____ power. increases (d) A smaller sample size _____ power. decreases
According to the Empirical Rule, 68% of the area under the normal curve is between μ−σ and μ+σ. What percent of the area under the normal curve is between μ and μ+σ?
34%
Find the probability of the indicated event if P(E)=0.40 and P(F)=0.50. Find P(E or F) if P(E and F)=0.05.
P(E or F)=. 85 --(.4) + (.5) - (.05) = .85
The mathematics section of a standardized college entrance exam had a mean of 19 and an SD of 5 for a recent year. Assume these are well modeled by a Normal distribution. a) About what percent of students scored over 31? b) About what percent of students scored under 16? c) About what percent of students scored between 16 and 31? --find z-score (score-mean)/(SD), use absolute value, then use z table (draw distribution, see if the area is the smaller, etc) -should sum to about 100
a) About 82% of students scored over 31. b) About 27.43% of students scored under 16. c) About 71.73% of students scored between 16 and 31.
Five sophomores were given an English achievement test before and after receiving instruction in basic grammar. Their scores are shown to the right. A researcher wonders if there's a difference between the Before and After scores. dependent t
a) Determine the mean. Use After−Before to compute the differences. -0.80 b) Calculate the appropriate SS:42.80 c) Calculate the appropriate standard deviation: 3.271 d) Calculate the appropriate standard error: 1.463 e) Calculate the appropriate (obtained/calculated) test statistic (z,t,r,F, etc): −0.547
Recent research suggests that 43% of residents from a certain region have a home phone, 95% have a cell phone, and 41% of people have both
a) The probability of a resident having a home or cell phone is . 97 -- (.41)+(.95)-(.41) b) The probability of a resident having neither a home phone nor a cell phone is 0.03 c) The probability of a resident having a cell phone but no home phone is . 54
Suppose that in a certain city voters are registered to vote in one of only two parties: 45%of the voters are registered as Democrats and 55%as Republicans You are conducting a poll by calling registered voters at random. In your first three calls, what are the following probabilities? Assume that every call is answered and that the process is completely random.
a) The probability of calling all Democrats is . 091.091. b) The probability of calling two Republicans is 0.408 --used binomial calculator
A confidence interval for a dependent samples t-test ranges from −9 to −3
a) What is the mean of the confidence interval? -6 b) If a researcher conducted a null hypothesis test to see if the two group means were the same, would the researcher reject or fail to reject the null hypothesis? reject Ho
Use the below source table to answer the following question.
a) What is the value of MSB (MSbetween)? 2968 a) What is the value of MSW (MSwithin)? 560
Compute the SS for the following data set. There are 3 groups, each with 2 scores. A B C 0 5 4 4 9 8
a) What is the value of k? 3 b) What is the grand mean? 5 c) What is the marginal mean for group A? 2 for B? 7 for C? 6 d) What is SSB (SSbetween)? 28 --sum of n(xbar - xdouble bar)^2 --n is number in each group e) What is SSW (SSwithin)? 24 --sum of (x - bar)^2 --each score f) What is SST (SStotal)? 52 --sum (x - xdouble bar)^2 --each score
The following questions (a through c) are about reporting two-sample t-tests in APA style. Some of the answers are very similar, so be sure to pay attention to details. The outcome variable is "Outcome X." Use α = .05 XbarA = 3.7 XbarB = 6.3 nA = 23 (sample size for Group A) nB = 23 (sample size for Group B) tobt = 2.855 IMPORTANT: The two groups are dependent/paired
a) Which of the following is a correct report of a(n) dependent/paired samples t-test in which the null hypothesis was REJECTED? Evidence suggests that Group B had a higher mean than Group A on Outcome X. b) And what is the correct APA-style report of a two-sample t-test in which the null hypothesis was REJECTED? t(22)= 2.855, p< .05. c) Now assume that the null hypothesis was RETAINED (not rejected). Which of the following is a correct report of a(n) dependent/paired samples t-test ? There's not enough evidence to suggest that Groups A and B differed on Outcome X.
A study was performed on teacher perceptions of the behavior of elementary school children. Teachers rated the aggressive behavior of a sample of 1450 New York City public school children by responding to the statement, "This child threatens or bullies others in order to get his/her own way." Responses were measured on a scale ranging from 1 (never) to 5 (always). The summary statistics were x=2.15 and s=1.05.Researchers wanted to test H0: μx=3 versus HA: μx≠3.Which of the following tests is the most appropriate to use (assuming all conditions for inference are satisfied)?
one-sample t-test A one-sample t-test is appropriate when the variable of interest is quantitative, there is one population, and the population standard deviation is not known
To study the effect of one factor on the mean of a response variable
one-way ANOVA
To study the effect of two factors on the mean of a response variable
two-way ANOVA