You have collected a simple random sample of 39 students. On average (the average here is measured by the sample mean), the students in your sample spent $600 on books in 2020. The lowest spending on the books among these 39 students in 2020 was $398. The greatest spending on the books among these 39 students in 2020 was $804. You want to estimate the population standard deviation of the amounts spent by students on books in 2020. Explain how you could find an approximate value of the population standard deviation from the information given here. Justify your assumptions. What is that approximate value of the population standard deviation?
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.
You have collected a simple random sample of 39 students. On average (the average here is measured by the sample mean), the students in your sample spent $600 on books in 2020. The lowest spending on the books among these 39 students in 2020 was $398. The greatest spending on the books among these 39 students in 2020 was $804. You want to estimate the population standard deviation of the amounts spent by students on books in 2020. Explain how you could find an approximate value of the population standard deviation from the information given here. Justify your assumptions. What is that approximate value of the population standard deviation?
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