A Midwest college admissions committee recently conducted a study to determine the relative debt incurred by students receiving their degrees in four years versus those taking more than four years. Some on the committee speculated a four-year student would likely be attending full time, whereas one taking more than four years could have a part-time job. However, average total debt provides only part of the information. Since the average, or mean, is affected by both large and small values, the committee also needed some way to determine the relative variances for the two groups. Samples of size 20 produced standard deviations of 2,636 for four-year graduates and 1,513 for those taking more than four years. Conduct a test of hypothesis to determine if the standard deviation of the debt for four-year graduates is larger than those taking more than four years. Use a significance level of 0.05.
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 Midwest college admissions committee recently conducted a study to determine the relative debt incurred by students receiving their degrees in four years versus those taking more than four years. Some on the committee speculated a four-year student would likely be attending full time, whereas one taking more than four years could have a part-time job. However, average total debt provides only part of the information. Since the average, or mean, is affected by both large and small values, the committee also needed some way to determine the relative variances for the two groups.
Samples of size 20 produced standard deviations of 2,636 for four-year graduates and 1,513 for those taking more than four years.
Conduct a test of hypothesis to determine if the standard deviation of the debt for four-year graduates is larger than those taking more than four years. Use a significance level of 0.05.
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