Suppose Laura, a facilities manager at a health and wellness company, wants to estimate the difference in the average amount of time that men and women spend at the company's fitness centers each week. Laura randomly selects 15 adult male fitness center members from the membership database and then selects 15 adult female members from the database. Laura gathers data from the past month containing logged time at the fitness center for these members. She plans to use the data to estimate the difference in the time men and women spend per week at the fitness center. The sample statistics are summarized in the table. Population Population description Population mean (unknown) Sample size Sample mean (min) Sample standard deviation (min) 11 male μ1 n=15 x¯1=137.7 s=51.7 22 female μ2 n=15 x¯2=114.6 s=34.2 df=24.283 The population standard deviations are unknown and unlikely to be equal, based on the sample data. Laura plans to use the two-sample ?-t-procedures to estimate the difference of the two population means, ?1−?2. compute the margin of error for the 99% confidence interval for the difference of the population means using software or a table of ?-distributions.t-distributions. If you are using software, you may find some software manuals helpful. Provide your answer precise to at least one decimal place.
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.
Suppose Laura, a facilities manager at a health and wellness company, wants to estimate the difference in the average amount of time that men and women spend at the company's fitness centers each week.
Laura randomly selects 15 adult male fitness center members from the membership database and then selects 15 adult female members from the database. Laura gathers data from the past month containing logged time at the fitness center for these members. She plans to use the data to estimate the difference in the time men and women spend per week at the fitness center. The sample statistics are summarized in the table.
| Population | Population description |
Population mean (unknown) |
Sample size |
Sample mean (min) |
Sample standard deviation (min) |
|---|---|---|---|---|---|
| 11 | male | μ1 | n=15 | x¯1=137.7 | s=51.7 |
| 22 | female | μ2 | n=15 | x¯2=114.6 | s=34.2 |
The population standard deviations are unknown and unlikely to be equal, based on the sample data. Laura plans to use the two-sample ?-t-procedures to estimate the difference of the two population means, ?1−?2.
compute the margin of error for the 99% confidence interval for the difference of the population means using software or a table of ?-distributions.t-distributions. If you are using software, you may find some software manuals helpful. Provide your answer precise to at least one decimal place.
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