i. Use an appropriate hypothesis test to determine whether the mean life satisfaction scores differ between the age groups. Test at two appropriate significance levels, stating clearly the hypotheses, the test statistic and its distribution under the null hypothesis. Comment on your findings. ii. State clearly any assumptions you made in part i. ii. Is it possible that there is no difference between older and younger adults in terms of their life satisfaction? Discuss.
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.
A study focused on the perception of life satisfaction that may vary between
older and younger people. For this reason, at random 12 adults over the age of 70 and 16 adults aged between 18 and 30 took a life satisfaction questionnaire that gave a score for each one of them (high values of the score indicate higher life satisfaction). Summaries of these scores are presented below.
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