Questions and Answers
Was this study an experiment or an observational study?
experiment
Would the researchers be justified in concluding that the D-cycloserine pill and two therapy sessions are as beneficial as eight therapy sessions without the pill?
no
Why might allowing therapists to choose who received D-cycloserine and who received the placebo lead to an incorrect conclusion?
because therapists might assign people with more severe acrophobia to one group and those with less severe acrophobia to the other group
Why might taking a convenience sample of the first 500 students at a football game be biased?
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How can a simple random sample of 500 students be implemented using a computer?
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Under what circumstances would stratification by campus provide a more precise estimate than by gender?
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Compare the distributions of concentration of aldrin among three rivers.
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The stemplot for River X reveals that there is a gap in the distribution of aldrin concentration between _____ and _____.
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Comment on any similarities and differences in the distributions of distances traveled by balls launched from catapult A and catapult B.
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Which catapult would be better to use for maximizing the probability of having ping-pong balls land within the band?
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How many centimeters from the target line should the chosen catapult be placed?
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If the manufacturer sets the mean distance traveled to be equal to 288 yards, what is the probability that a ball will travel too far?
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What is the probability that at least one of five independently tested balls will exceed the maximum distance of 291.2 yards?
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What is the largest mean distance that can be used to ensure 99 percent certainty that a ball will not exceed 291.2 yards?
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What was the response variable in the draft study?
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Was randomization used properly in the hitch study?
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Was replication used properly in this study?
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Why is the plot of land considered a confounding variable in this experiment?
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Why is the probability distribution of X not binomial?
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What is the probability that all 4 in the sample to be tested are male?
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Do you think that males and females were equally represented in the group of 20 brontosaurs stuck in the swamp?
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Is it reasonable to generalize your conclusion about the group of 20 brontosaurs to the population of all brontosaurs?
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Based on the students' sample, is there support for their belief that the proportion of boxes with vouchers is less than 0.2?
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What is the probability that randomly selecting 3 people from a group of 6 men and 3 women will result in selecting 3 women?
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Is there reason to doubt the manager's claim that the 3 people were selected at random?
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Does the proposed process correctly simulate the random selection of 3 women from a group of 9 people?
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Is a line an appropriate model to use for the data on commercial aircraft from 1990-1998?
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What is the value of the slope of the least squares regression line for commercial aircraft data?
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What is the value of the intercept of the least squares regression line?
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What is the predicted number of commercial aircraft flying in 1992?
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What was the actual number of commercial aircraft flying in 1992?
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What does the 95% confidence level mean in the context of dog ownership in households?
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Does the humane society's interval estimate provide evidence that the proportion of dog owners in its county is different from the claimed national proportion?
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How many households were selected in the humane society's sample?
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What proportion of crows in the sample had lead levels classified as unhealthy?
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Construct and interpret a 95% confidence interval for the mean level of lead in crows.
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What is the probability that a person chosen at random from a sample will be in the 31-45 age category?
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What is the probability that a person chosen at random whose incomes are over $50,000 will be in the 31-45 category?
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Is annual income independent of age category for those in this sample?
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What is the probability that the weight of the ore in a randomly selected car will be 70.7 tons or more?
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If the weight of ore in a randomly selected car is 70.7 tons, would that fact make you suspect the loading mechanism is overfilling?
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What is the probability that a random sample of 10 cars have a mean ore weight of 70.7 tons or more?
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If a random sample of 10 cars had a mean ore weight of 70.7, would you suspect that the loading mechanism was overfilling?
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Study Notes
Sampling Methods in Surveys
- Convenience sampling, like using students at a football game, may introduce bias, as attendees may have stronger school pride affecting their satisfaction ratings.
- Simple random sampling involves assigning numbers to each student and using a random number generator to select participants, ensuring a true random representation.
- Stratification can enhance estimation accuracy; stratifying by campus is preferable if opinions vary more between campuses than by gender.
Environmental Cleanup Study
- Three rivers were sampled for aldrin pesticide concentration, showing River X had the highest median and skewed distribution.
- River Y displayed symmetry, while River Z had a slightly left-skew. The distributions differed significantly across all three rivers.
- Stemplots can reveal more detailed characteristics, such as gaps in distribution, which may not be apparent in boxplots.
Toy Catapult Experiment
- Both catapults showed approximately symmetrical and unimodal distributions, but Catapult A had a lower median and outliers compared to Catapult B.
- Catapult B is preferable for maximizing chances of hitting the target due to lower variability in distances.
- The optimal distance for Catapult B from the target line is 138 cm, reflecting its symmetric distance distribution centered there.
Golf Ball Manufacturing Standards
- Golf balls must adhere to a maximum distance of 291.2 yards; manufacturers seek to optimize mean travel distance without surpassing it.
- If mean distance is set to 288 yards, the probability of exceeding distance limits is approximately 12.71%.
- Testing five balls shows a probability of 49.32% that at least one will exceed limits, emphasizing the risks in quality control.
- A mean distance of approximately 284.68 yards ensures a 99% certainty that balls won't surpass the threshold.
Tractor Draft Study
- The study assessed draft (energy needed to pull) to compare standard vs. new hitches, with 25 measurements taken for each hitch's performance.
- The response variable was draft, and treatments included standard and new hitches. Experimental units were the land plots used.
- Randomization was applied correctly as treatments were assigned to specific plots.
- However, replication was insufficient since each treatment was only tested on one plot, limiting the ability to detect consistent patterns.
- Plot variability could confound results, as differences in draft may arise from varying soil or conditions rather than hitch effectiveness.
Brontosaur DNA Testing
- Sampling 20 femur bones without replacement for gender analysis creates a non-binomial distribution, as trials aren't independent due to reduced population size after selections.
- Probability calculations show a 4/20 chance of sampling exclusively males if the population consists of 10 males and 10 females; this outcome may suggest a potential bias in representation if such a result is noted in tests.### General Probability and Sampling Concerns
- Observing a small probability for males in cases of equal representation indicates potential sampling issues.
- In archaeological studies, a sample of brontosaur bones may be biased and not representative of all brontosaurs due to preservation conditions in specific environments.
Statistical Evidence and Testing Hypotheses
- A group of students tested the claim that 20% of cereal boxes contain vouchers. They found only 11 out of 65 boxes (16.9%).
- Hypothesis testing involved setting the null hypothesis (p=0.2) and alternative hypothesis (p<0.2). Findings did not provide convincing evidence to reject the null hypothesis.
- The probability of selecting 3 women from 9 sales representatives (6 men, 3 women) randomly is low (1.2%), suggesting possible bias in the selection method.
Regression Analysis in Air Travel Data
- A residual plot with no discernible pattern supports using a linear model for air travel data between 1990-1998.
- The slope of the least squares regression line indicates an average increase of approximately 233.517 commercial aircraft annually.
- The intercept value suggests that approximately 2939.93 aircraft were flying in the year 1990.
Confidence Intervals in Household Dog Ownership
- A 95% confidence level suggests that if repeated samples were taken, 95% would capture the true proportion of dog-owning households.
- The confidence interval for dog ownership (0.298 to 0.536) includes the national claim of 39%, indicating no significant difference.
- A sample size for the dog ownership study was calculated to be approximately 66 households.
Environmental Lead Levels in Crows
- 17.4% of crows in a sampled group had unhealthy lead levels exceeding 6 ppm.
- A 95% confidence interval for the mean lead level was calculated as (4.416 ppm, 5.384 ppm), indicating the average lead exposure in the population.
Analysis of Income and Age Categories
- The probability of selecting an individual aged 31-45 from a sample is calculated as approximately 42.99%.
- Probability analysis shows income is not independent of age categories in the suburban sample, as probabilities for age groups differ based on income thresholds.
Weight of Bauxite Ore
- In normal distribution, the probability of a single car weighing 70.7 tons or more is about 21.77%.
- A sample mean of 70.7 tons for 10 cars has a low probability (0.69%), suggesting potential overfilling of the cars if such a result occurs.
Experimental Study on Acrophobia
- The study involving D-cycloserine was an experiment, as researchers imposed treatments on participants with acrophobia.
- Statistical results showed that D-cycloserine combined with fewer therapy sessions led to more improvement than placebo, but there was no comparable group for just therapy.
- Improper assignment of subjects to treatment groups could confound results, as initial severity of acrophobia might influence outcomes.
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Description
Explore the distinctions between experimental and observational studies in psychology. This quiz examines the implications of therapy sessions on treatment outcomes and the potential biases introduced when therapists decide treatment assignments. Engage with thought-provoking questions about research design and conclusions.