People tend to evaluate the quality of their lives relative to others around them. In a demonstration of this phenomenon, Frieswijk, Buunk, Steverink, and Slaets (2004) conducted interviews with frail elderly people. In the interview, each person was compared with fictitious others who were worse off. After the interviews, the elderly people reported more satisfaction with their own lives. Following are hypothetical data similar to those obtained in the research study. The scores are measures on a life-satisfaction scale for a sample of n = 9 elderly people who completed the interview. Assume that the average score on this scale is µ = 20. Are the data sufficient to conclude that the people in this sample are significantly more satisfied than others in the general population? Use a one-tailed test with α = .05. The life-satisfaction scores for the sample are 18, 23, 24, 22, 19, 27, 23, 26, 25. Report the estimated d and r2 and give an interpretation of each.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
- People tend to evaluate the quality of their lives relative to others around them. In a demonstration of this phenomenon, Frieswijk, Buunk, Steverink, and Slaets (2004) conducted interviews with frail elderly people. In the interview, each person was compared with fictitious others who were worse off. After the interviews, the elderly people reported more satisfaction with their own lives. Following are hypothetical data similar to those obtained in the research study. The scores are measures on a life-satisfaction scale for a sample of n = 9 elderly people who completed the interview. Assume that the average score on this scale is µ = 20. Are the data sufficient to conclude that the people in this sample are significantly more satisfied than others in the general population? Use a one-tailed test with α = .05. The life-satisfaction scores for the sample are 18, 23, 24, 22, 19, 27, 23, 26, 25. Report the estimated d and r2 and give an interpretation of each.
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