Gender Wage Gap It has long been a concern that there is a wage gap between men and women in the United States with some reports suggesting that women only make \$0.77 for every dollar earned by a man. Design a study that would allow you to confirm whether a wage gap does actually exist.
Table of contents
- 1. Intro to Stats and Collecting Data1h 14m
- 2. Describing Data with Tables and Graphs1h 55m
- 3. Describing Data Numerically2h 5m
- 4. Probability2h 16m
- 5. Binomial Distribution & Discrete Random Variables3h 6m
- 6. Normal Distribution and Continuous Random Variables2h 11m
- 7. Sampling Distributions & Confidence Intervals: Mean3h 23m
- Sampling Distribution of the Sample Mean and Central Limit Theorem19m
- Distribution of Sample Mean - Excel23m
- Introduction to Confidence Intervals15m
- Confidence Intervals for Population Mean1h 18m
- Determining the Minimum Sample Size Required12m
- Finding Probabilities and T Critical Values - Excel28m
- Confidence Intervals for Population Means - Excel25m
- 8. Sampling Distributions & Confidence Intervals: Proportion1h 25m
- 9. Hypothesis Testing for One Sample3h 29m
- 10. Hypothesis Testing for Two Samples4h 50m
- Two Proportions1h 13m
- Two Proportions Hypothesis Test - Excel28m
- Two Means - Unknown, Unequal Variance1h 3m
- Two Means - Unknown Variances Hypothesis Test - Excel12m
- Two Means - Unknown, Equal Variance15m
- Two Means - Unknown, Equal Variances Hypothesis Test - Excel9m
- Two Means - Known Variance12m
- Two Means - Sigma Known Hypothesis Test - Excel21m
- Two Means - Matched Pairs (Dependent Samples)42m
- Matched Pairs Hypothesis Test - Excel12m
- 11. Correlation1h 24m
- 12. Regression1h 50m
- 13. Chi-Square Tests & Goodness of Fit2h 21m
- 14. ANOVA1h 57m
10. Hypothesis Testing for Two Samples
Two Means - Matched Pairs (Dependent Samples)
Problem 11.2.5c
Textbook Question
Naughty or Nice? An experiment was conducted in which 16 ten-month-old babies were asked to watch a climber character attempt to ascend a hill. On two occasions, the baby witnesses the character fail to make the climb. On the third attempt, the baby witnesses either a helper toy push the character up the hill, or a hinderer toy preventing the character from making the ascent. The helper and hinderer toys were shown to each baby in a random fashion for a fixed amount of time. In Problem 41 from Section 10.2, we learned that, after watching both the helper and hinderer toy in action, 14 of 16 ten-month-old babies preferred to play with the helper toy when given a choice as to which toy to play with. A second part of this experiment showed the climber approach the helper toy, which is not a surprising action, and then alternatively the climber approached the hinderer toy, which is a surprising action. The amount of time the ten-month-old watched the event was recorded. The mean difference in time spent watching the climber approach the hinderer toy versus watching the climber approach the helper toy was 1.14 seconds with a standard deviation of 1.75 second. Source: J. Kiley Hamlin et al., “Social Evaluation by Preverbal Infants,” Nature, Nov. 2007.
c. What do you think the results of this experiment imply about 10-month-olds’ ability to assess surprising behavior?
Verified step by step guidance1
Step 1: Understand the context of the experiment. The babies watched two scenarios: the climber approaching the helper toy (expected behavior) and the climber approaching the hinderer toy (surprising behavior). The time spent watching each event was recorded, and the difference in watching times was calculated.
Step 2: Recognize that the mean difference in watching time (hinderer approach minus helper approach) is 1.14 seconds, with a standard deviation of 1.75 seconds. This suggests babies spent more time watching the surprising event (approach to hinderer) on average.
Step 3: Interpret the implication of longer looking times. In developmental psychology, longer looking times often indicate that infants detect something unexpected or surprising, showing increased attention or cognitive processing.
Step 4: Connect the statistical results to the babies' cognitive abilities. Since the babies looked longer at the surprising behavior, it implies they can distinguish between expected and unexpected social actions, suggesting an early ability to assess social behavior.
Step 5: Summarize that the experiment's results imply 10-month-old babies have some capacity for social evaluation, as evidenced by their differential attention to surprising versus expected behaviors.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Hypothesis Testing
Hypothesis testing is a statistical method used to decide whether there is enough evidence to support a specific claim about a population. In this experiment, it helps determine if the difference in watching times for surprising versus expected behavior is statistically significant, indicating infants’ ability to detect surprising actions.
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Mean Difference and Standard Deviation
The mean difference measures the average change between two related observations, such as time spent watching different events. The standard deviation quantifies the variability of these differences, showing how consistent the infants’ responses are across the sample.
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Infant Cognitive Development and Social Evaluation
This concept relates to how infants perceive and interpret social interactions, such as distinguishing helpful versus hindering behavior. The experiment’s results suggest that even at 10 months, babies can assess and react to surprising or unexpected social actions, indicating early cognitive and social evaluation abilities.
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