5.3-9.2 (exam review)
Nia suggests all students be given both a caffeine pill and a placebo, but the order be randomized. Students' performances on both these occasions should then be recored.
- Experimental study - paired
Mimi suggests the students be paired by height, and then one student in each pair is randomly assigned to caffeine while the other isn't
- experimental study - paired design
The validity condition for a chi-square test is that all cells of the table should have at least ___ observations
10
Validity conditions for the theory-based approach to a two sample proportions test require that each explanatory variable group has at least ___ observations in each category of the response variable. Or simply put, ___ number in each level of the independent variable
10
With regards to the videos/reading on "Coming to a Stop", did the study pair observational units in one group with observational units in another group or are the observational units in the different groups independent?
Independent
A null hypothesis of no association implies that all means being compared across multiple groups are equal
True
An F-statistic is the ratio of "between group variability" and "within group variability'
True
If the null hypothesis is rejected when doing an ANOVA, it is appropriate to do a follow-up comparing the different group means to each other
True
In a matched paired design, there will always be the same number of people in group one as group two
True
Which of the following statements is true of the stimulation-based approach for paired data?
We randomly determine whether or not to swap the two values in each pair since our assumption is that it does not matter which is which
When comparing multiple proportions, what hypothesis can be expressed as saying that at least one population proportion differs from the others?
alternative hypothesis
The theory-based approach for two proportions
can be used to estimate p-value and confidence intervals
With regards to the videos/reading on "Coming to a Stop", is the variable whether the vehicle comes to a complete stop categorical or quantitative?
categorial with 2 categories (binary)
With regards to the videos/reading on "Coming to a Stop", is the variable arrival position categorical or quantitative?
categorial with 3 categories
What are used as a follow-up to the ANOVA analysis?
confidence intervals
As long as the sample size within each of the multiple groups being compared is at least 20, ANOVA is acceptable to run
false
What consists of the minimum, lower quartile, median, upper quartile, and maximum?
five-number summary
What does the acronym MAD stand for?
mean of absolute differences
Is the average body temperature higher than 98.6°F? IV: people in general DV: temperature (F)
one mean
Larger values of the F-statistic provide ___ evidence against the null hypothesis.
stronger
larger values of the chi-square statistic provide ___ evidence against the null hypothesis
stronger
What does the alternative hypothesis imply in a test of two sample mean?
that there is an association between the two variables
For the two sample proportions test what is the statistic of interest?
the difference in conditional proportions
For a class project, statistics students asked students in their class (30 students) how many hours of sleep they had gotten the night before, and also recorded each students gender. The students found that the average sleep hours for the 12 males in the class was 5.8 hours with a standard deviation of 1.5 and for the 18 females in the class was 6.5 hours with a standard deviation of 1.2 hours. The distributions of sleep hours were fairly symmetric for both males and females. The students were interested in learning whether males and females at their school tend to get different amounts of sleep on average. - When applying the 3-S strategy to this data, the statistic is - in the simulation, you should have - after shuffling the slips of paper you should deal the slips into
- 0.7 hours - 30 slips of paper total and the sleep time for the student written on each slip of paper - One pile of 18 slips and one pile of 12
When studying quantitative (numeric) data, which of the following should we examine?
- Medians of the distributions if skewed - variability of the distributions (standard deviation) - center of the distributions (mean)
For a class project, statistics students asked students in their class (30 students) how many hours of sleep they had gotten the night before, and also recorded each students gender. The students found that the average sleep hours for the 12 males in the class was 5.8 hours with a standard deviation of 1.5 and for the 18 females in the class was 6.5 hours with a standard deviation of 1.2 hours. The distributions of sleep hours were fairly symmetric for both males and females. The students were interested in learning whether males and females at their school tend to get different amounts of sleep on average. - A 95% confidence interval for the difference in average sleep time is (-0.38, 1.78). Thus, the p-value for the corresponding two-sided of significance will be - The theory-based test is ? - A 95% confidence interval for the difference in average sleep times is (-0.38, 1.78) means that we're 95% confident that the true average difference in sleep times between males and females at your school is between -0.38 and 1.78 hours.
- more than 0.05 - valid - True
Lara suggest the instructor record everyone's performance on a long jump, and then ask each of them to report their caffeine intake from earlier in the day.
- observational study - unpaired
A theory-based test comparing two proportions is valid when
- the sample size is large - there are at least 10 observations in each of the 4 cells of the two-way table
How does increased sample size effect the following
- width of the 95% confidence interval - gets smaller - midpoint of the 95% confidence inter - stays the same - p-value - gets smaller - the absolute value of the standardized statistic - gets larger
The validity conditions for a two sample means test are met if the distributions in both populations are not strongly skewed and the sample sizes in each group are at least ___
20
What is the inter-quartile range for the following 5 number summary Min=0, lower quartile=2, median=5, upper quartile=10, maximum=20?
8
Suppose you are testing the hypotheses H0: μd = 0 and Ha: μd ≠ 0 in a paired test and obtain a p-value of 0.02. Also suppose you computed confidence intervals for μd. Based on the p-value which of the following is true?
A 95% confidence interval will not contain 0, but a 99% confidence interval will
larger values of the ___ statistic provide stronger evidence that the multiple population means are not all the same.
F-statisitic
An alternative hypothesis of association implies that all means being compared across multiple groups are different
False
The MAD statistic can be used for both simulation and theory-based approaches, no alternative statistic is needed
False
The null distribution of the MAD statistic will be a bell-shaped curve, centered at zero
False
When a chi-squared test provides strong evidence against the null hypothesis, it says all the population proportions differ significantly from each other
False
With regards to the videos/reading on "coming to a stop", did the study make use of random sampling, random assignment, both or neither?
Neither
Does the following study involve paired or unpaired data? A researcher compares weight change for a group of students from the beginning of their freshman year to the end of their freshman year
Paired data
Which of the following if true of the validity conditions for the paired t-test/
The population distribution of differences should be symmetric, or your sample should have at least 20 pairs and the distribution of sample differences should not be strongly skewed
In general, large values of the MAD statistic provide strong evidence against the null hypothesis
True
Pairing is advantageous because it reduces unwanted variability, improving statistical power
True
The MAD statistic can be used when comparing group means or group proportions
True
The following five number summary suggests that the dataset is right skewed, Min=0, lower quartile=2, median=5, upper quartile=10, maximum=20
True
The lower quartile will always be inclusively between the minimum value of the dataset and the median
True
The main reason for comparing multiple groups using the MAD statistic or ANOVA instead of using methods learned in Chapter 6 (e.g., independent samples t-test comparing two groups) comparing all possible pairs of groups to each other is to minimize the chance of a Type I error.
True
True or False? Ho: πsingle = πlead = πfollow is a valid way of writing the null hypothesis when comparing multiple proportions.
True
When calculating a confidence interval for both a two sample proportions test and a two sample means test, one of the most notable characteristics is whether or not it includes zero.
True
A school cafeteria offers a vegetarian and a nonvegetarian option for lunch every day. For a period of two weeks, you record how many calories are in the vegetarian option and how many calories are in the nonvegetarian option. Your goal is to see if vegetarian options tend to diff er with regard to average number calories from nonvegetarian options.
a paired analysis is appropriate
A farmer investigates whether talking to cows by name leads to producing more milk. He randomly selects 30 of his cows and randomly assigns 15 to talk to by name and the other 15 not to.
a paired analysis is not appropriate
When a chi-square test reveals strong evidence against the null hypothesis, what are used to determine which pairs of groups differ significantly?
confidence intervals
Larger values of the MAD statistic indicate a ____ difference in sample proportions across groups and thus provide ____ evidence against the null hypothesis.
greater, stronger
20 golfers are paired up based on their ability level. One member of each pair of golfers plays a round with one type of golf ball, and the other member of the pair with a different type of golf ball.
matched pairs
If paired data is incorrectly analyzed using an independent groups approach, the null distribution will typically have
more variability than when analyzed as paired data
When comparing multiple means, which hypothesis says that the populations means of the response variable are identical for all categories of the explanatory variabel/
null hypothesis
The purpose of the study is to determine if males gain more than the average amount
one mean (test of signficance)
If individuals are weighed before beginning a weight loss program, and again at the end of the weight loss program this is an example of a
paired study design
Will rats go through a maze faster after given caffeine compared to the same rats without caffeine? IV: treatment: caffeine, no caffeine (same rat) DV: run through maze faster (time)
paired test
School-children's heights from one-year ago are being compared to their heights today
repeated measures pairs
The standardized statistic for a difference in sample means is called what?
standardized t-statistic
What is the statistic of interest in a two sample means test?
the difference in sample means between the two groups
Is there an association between a person's gender and GPA? IV: Gender(male, female) DV: GPA
two mean
The purpose of the study is to determine if Gender (male, female) impacts weights gain (in pounds).
two mean
Is there an association between a person's gender and whether or not a person gets the flu? IV: Gender (male, female) DV: flue: yes, no
two proportion
The purpose of the study is to determine if Gender (male, female) impacts weights gain: high, low
two proportion
A researcher compares exercise habits for a group of students who are athletes compared to students who are not athletes.
unpaired data
What is the value for which 25% of the data lie about it called?
upper quartile
The validity conditions for ANOVA are that all sample sizes are at least 20 or that the distribution is approximately normal and that all populations have approximately the same ___
variability
