In the Preview for Chapter 2, we presented a study showing that a woman shown in a photograph was judged as less attractive when the photograph showed a visible tattoo compared to the same photograph with the tattoo removed (Resenhoeft, Villa, & Wiseman, 2008). Suppose a similar experiment is conducted as a repeated-measures study. A sample of n = 12 males looks at a set of 30 photographs of women and rates the attractiveness of each woman using a 5-point scale (5 = most positive). One photograph appears twice in the set, once with a tattoo and once with the tattoo removed. For each participant, the researcher records the difference between the two ratings of the same photograph. On average, the photograph without the tattoo is rated MD = 1.2 points higher than the photograph with the tattoo, with SS = 33 for the difference scores. Does the presence of a visible tattoo have a significant effect on the attractiveness ratings? Use a two-tailed test with α = .05. For this problem, complete the four stages of hypothesis testing: (1) Identify the two hypotheses (2) Determine the critical region for your decision (3) Compute the test statistic (4) Use the test statistic to make a decision and interpret that decision
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.
In the Preview for Chapter 2, we presented a study showing that a woman shown in a photograph was judged as less attractive when the photograph showed a visible tattoo compared to the same photograph with the tattoo removed (Resenhoeft, Villa, & Wiseman, 2008). Suppose a similar experiment is conducted as a repeated-measures study. A sample of n = 12 males looks at a set of 30 photographs of women and rates the attractiveness of each woman using a 5-point scale (5 = most positive). One photograph appears twice in the set, once with a tattoo and once with the tattoo removed. For each participant, the researcher records the difference between the two ratings of the same photograph. On average, the photograph without the tattoo is rated MD = 1.2 points higher than the photograph with the tattoo, with SS = 33 for the difference scores. Does the presence of a visible tattoo have a significant effect on the attractiveness ratings? Use a two-tailed test with α = .05. For this problem, complete the four stages of hypothesis testing:
(1) Identify the two hypotheses
(2) Determine the critical region for your decision
(3) Compute the test statistic
(4) Use the test statistic to make a decision and interpret that decision
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