a. Use an independent-measures t test with a = .05 to determine whether there is a significant difference between the two conditions and compute r² to measure effect size. b. Now, increase the variability by doubling the two SS values to SS1 = 1,020 and SS2 = 828. || Repeat the hypothesis test and the measure of effect size. c. Comparing your answers for Parts a and b, describe how sample variability influences the outcome of the hypothesis test and the measure of effect size.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
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![### Hypothesis Testing and Sample Variability
**a.** Use an independent-measures t test with \( \alpha = .05 \) to determine whether there is a significant difference between the two conditions and compute \( r^2 \) to measure effect size.
**b.** Now, increase the variability by doubling the two SS values to \( SS_1 = 1,020 \) and \( SS_2 = 828 \). Repeat the hypothesis test and the measure of effect size.
**c.** Comparing your answers for [Parts a and b](#), describe how sample variability influences the outcome of the hypothesis test and the measure of effect size.
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![In 1974, Loftus and Palmer conducted a classic study demonstrating how the language used to ask a question can influence eyewitness memory. In the study, college students watched a film of an automobile accident and then were asked questions about what they saw. One group was asked, “About how fast were the cars going when they smashed into each other?” Another group was asked the same question except the verb was changed to “hit” instead of “smashed into.” The “smashed into” group reported significantly higher estimates of speed than the “hit” group. Suppose a researcher repeats this study with a sample of today’s college students and obtains the following results:
A table titled "Estimated Speed" contains the results:
- **Smashed into**
- Sample size (\(n\)) = 15
- Mean estimated speed (\(M\)) = 40.8
- Sum of squares (\(SS\)) = 510
- **Hit**
- Sample size (\(n\)) = 15
- Mean estimated speed (\(M\)) = 34.9
- Sum of squares (\(SS\)) = 414](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc42d87a0-298c-4581-9ff7-d7fc87785846%2F423dd244-83d0-4560-a546-473565575058%2Fxum7xnt_processed.png&w=3840&q=75)
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