Research Methods in Psychology
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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?

<p>The first 500 students do not represent the whole population of the school. It is likely that most of those students that attended the football game have school pride, which could be related to their opinion about how the school looks.</p> Signup and view all the answers

How can a simple random sample of 500 students be implemented using a computer?

<p>Get a list of all 70,000 students at the university and give each one a number from 1 to 70,000. Then use a computer to generate 500 random integers from between 1 and 70,000 without replacement. The students whose numbers are picked are selected for the sample.</p> Signup and view all the answers

Under what circumstances would stratification by campus provide a more precise estimate than by gender?

<p>Stratifying by campus would be beneficial over stratifying by gender if the opinions about the school's appearance differ more between the two campuses than by gender.</p> Signup and view all the answers

Compare the distributions of concentration of aldrin among three rivers.

<p>The median concentration of aldrin tends to be highest for River X and lowest for River Z. About 50% of the concentrations of aldrin for River X and River Y are higher than all of the concentrations of River Z. River X is skewed right, River Y is roughly symmetric, and River Z is slightly skewed left.</p> Signup and view all the answers

The stemplot for River X reveals that there is a gap in the distribution of aldrin concentration between _____ and _____.

<p>5.6, 7.3</p> Signup and view all the answers

Comment on any similarities and differences in the distributions of distances traveled by balls launched from catapult A and catapult B.

<p>Both distributions are roughly symmetrical and unimodal. The center (median) of A is slightly less than catapult B. Catapult A has a few outliers while catapult B does not.</p> Signup and view all the answers

Which catapult would be better to use for maximizing the probability of having ping-pong balls land within the band?

<p>Catapult B would be the best because the distances vary less from the center of the distribution.</p> Signup and view all the answers

How many centimeters from the target line should the chosen catapult be placed?

<p>The catapult should be placed 138 cm from the target line.</p> Signup and view all the answers

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?

<p>P(D&gt;291.2) = P(z&gt;(291.2-288)/(2.8)) = P(z&gt;1.14) = 1 - 0.8729 = 0.1271</p> Signup and view all the answers

What is the probability that at least one of five independently tested balls will exceed the maximum distance of 291.2 yards?

<p>1 - (1 - 0.1271)^5 = 0.4932</p> Signup and view all the answers

What is the largest mean distance that can be used to ensure 99 percent certainty that a ball will not exceed 291.2 yards?

<p>M = 284.676</p> Signup and view all the answers

What was the response variable in the draft study?

<p>The amount of draft.</p> Signup and view all the answers

Was randomization used properly in the hitch study?

<p>Yes, the two hitches were randomly assigned to the two land plots.</p> Signup and view all the answers

Was replication used properly in this study?

<p>No, each treatment was applied to only one experimental unit.</p> Signup and view all the answers

Why is the plot of land considered a confounding variable in this experiment?

<p>Even though 25 measurements were taken at different locations on the two plots, each hitch was used on one plot only. Thus, if a difference in the draft is observed we will not know whether the difference is because of the hitch or the plot.</p> Signup and view all the answers

Why is the probability distribution of X not binomial?

<p>X is not binomial because the trials are not independent and the conditional probabilities change at each trial due to sampling without replacement.</p> Signup and view all the answers

What is the probability that all 4 in the sample to be tested are male?

<p>(10/20)<em>(9/19)</em>(8/18)*(7/17) = 0.043</p> Signup and view all the answers

Do you think that males and females were equally represented in the group of 20 brontosaurs stuck in the swamp?

<p>No</p> Signup and view all the answers

Is it reasonable to generalize your conclusion about the group of 20 brontosaurs to the population of all brontosaurs?

<p>No</p> Signup and view all the answers

Based on the students' sample, is there support for their belief that the proportion of boxes with vouchers is less than 0.2?

<p>No, there is not convincing evidence.</p> Signup and view all the answers

What is the probability that randomly selecting 3 people from a group of 6 men and 3 women will result in selecting 3 women?

<p>(3/9)<em>(2/8)</em>(1/7) = 0.012</p> Signup and view all the answers

Is there reason to doubt the manager's claim that the 3 people were selected at random?

<p>Yes</p> Signup and view all the answers

Does the proposed process correctly simulate the random selection of 3 women from a group of 9 people?

<p>No</p> Signup and view all the answers

Is a line an appropriate model to use for the data on commercial aircraft from 1990-1998?

<p>Yes</p> Signup and view all the answers

What is the value of the slope of the least squares regression line for commercial aircraft data?

<p>233.517</p> Signup and view all the answers

What is the value of the intercept of the least squares regression line?

<p>2939.93</p> Signup and view all the answers

What is the predicted number of commercial aircraft flying in 1992?

<p>3406.964</p> Signup and view all the answers

What was the actual number of commercial aircraft flying in 1992?

<p>3446.954</p> Signup and view all the answers

What does the 95% confidence level mean in the context of dog ownership in households?

<p>It means that if random samples of the same size were taken repeatedly, about 95% of the intervals would capture the true population proportion.</p> Signup and view all the answers

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?

<p>No</p> Signup and view all the answers

How many households were selected in the humane society's sample?

<p>65.95</p> Signup and view all the answers

What proportion of crows in the sample had lead levels classified as unhealthy?

<p>0.174</p> Signup and view all the answers

Construct and interpret a 95% confidence interval for the mean level of lead in crows.

<p>(4.416, 5.384)</p> Signup and view all the answers

What is the probability that a person chosen at random from a sample will be in the 31-45 age category?

<p>0.42995</p> Signup and view all the answers

What is the probability that a person chosen at random whose incomes are over $50,000 will be in the 31-45 category?

<p>0.36458</p> Signup and view all the answers

Is annual income independent of age category for those in this sample?

<p>No</p> Signup and view all the answers

What is the probability that the weight of the ore in a randomly selected car will be 70.7 tons or more?

<p>0.2177</p> Signup and view all the answers

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?

<p>No</p> Signup and view all the answers

What is the probability that a random sample of 10 cars have a mean ore weight of 70.7 tons or more?

<p>0.0069</p> Signup and view all the answers

If a random sample of 10 cars had a mean ore weight of 70.7, would you suspect that the loading mechanism was overfilling?

<p>Yes</p> Signup and view all the answers

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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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.

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