our sister, Tina, believes that consuming energy drinks after 4 p.m. makes it difficult for people to sleep at night. She knows that the population average of hours of sleep that people get is p = 7 hours. One day, while hanging out with her friends at 4p.m., she buys energy drinks for her friends and they drink it. The next day, Tina asks them how many hours they slept that night. (clarice - 5, mei - 4, tony - 6, philip - 4, zina - 3, po - 5, felix - 4) a.) Calculate the mean, sum of squares, variance, and estimated standard error of the mean. Show the calculations and clearly indicate the final answers. b.) Conduct the appropriate hypothesis test to determine whether people who consume energy drinks after 4 p.m. get less sleep at night. Use α = .05. c.) Zina got very little sleep the night before and was confused why Tina did not just use a z-test. Explain to Zina why Tina did not use a z-test. d.) In a short paragraph, give Tina’s friend a brief summary of the hypothesis test and results. Be specific to the situation. What were the predictions? Did the observed mean in the sample reflect a real mean difference in the population? Can chance/error be ruled out? e.) How does the hypothesized distribution used to test Tina’s hypothesis change as sample size increases? Write a brief explanation and draw a rough sketch to illustrate.
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.
Your sister, Tina, believes that consuming energy drinks after 4 p.m. makes it difficult for people to sleep at night. She knows that the population average of hours of sleep that people get is p = 7 hours. One day, while hanging out with her friends at 4p.m., she buys energy drinks for her friends and they drink it. The next day, Tina asks them how many hours they slept that night. (clarice - 5, mei - 4, tony - 6, philip - 4, zina - 3, po - 5, felix - 4)
a.) Calculate the mean, sum of squares, variance, and estimated standard error of the mean. Show the calculations and clearly indicate the final answers.
b.) Conduct the appropriate hypothesis test to determine whether people who consume energy drinks after 4 p.m. get less sleep at night. Use α = .05.
c.) Zina got very little sleep the night before and was confused why Tina did not just use a z-test. Explain to Zina why Tina did not use a z-test.
d.) In a short paragraph, give Tina’s friend a brief summary of the hypothesis test and results. Be specific to the situation. What were the predictions? Did the observed mean in the sample reflect a real mean difference in the population? Can chance/error be ruled out?
e.) How does the hypothesized distribution used to test Tina’s hypothesis change as sample size increases? Write a brief explanation and draw a rough sketch to illustrate.
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