Question : The Epworth Sleepiness Scale (ESS) was designed to measure whether a person is getting enough sleep. The test asks such questions as how likely you are to doze off in a variety of situations, such as watching TV, or at a meeting, or even as a passenger in a car on a long ride. The test is designed to produce a mean score of 7.50. A random sample of college students was selected and the following scores were obtained: 6, 10, 4, 3, 8, 12, 5, 7, 9, 4, 10, 2, 7, 5, 4, 7, 8, 11, 3, 7. Could this sample be representative of a population whose mean is 7.50? Conduct the hypothesis testing (show all the six steps of hypothesis testing) using α = .05 and the two-tailed test. Give the probability statement after the statistical test is done.
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.
Question : The Epworth Sleepiness Scale (ESS) was designed to measure whether a person is getting enough sleep. The test asks such questions as how likely you are to doze off in a variety of situations, such as watching TV, or at a meeting, or even as a passenger in a car on a long ride. The test is designed to produce a mean score of 7.50. A random sample of college students was selected and the following scores were obtained: 6, 10, 4, 3, 8, 12, 5, 7, 9, 4, 10, 2, 7, 5, 4, 7, 8, 11, 3, 7. Could this sample be representative of a population whose mean is 7.50? Conduct the hypothesis testing (show all the six steps of hypothesis testing) using α = .05 and the two-tailed test. Give the probability statement after the statistical test is done.
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