Mathcorp has 35,000 employees and claims that the average salary is $50,000. You are an investigative journalist who wants to know what the average salary actually is for a Mathcorp employee, but the company does not publically post their budget or salaries. You post a question on popular online message board Read It, and 57 employees respond. However, you can only verify 36 of the results after calling Mathcorp and speaking with the employee directly on the phone. You decide to use these 36 people as your sample. After collecting the results into a spreadsheet, you run the calculation and find out that the mean average salary is $45,215.15291. You decide to just round that to $45,215. Furthermore, after rounding, the standard deviation of your sample is $9,512. question Run a full hypothesis test with a significance level of 5%. Interpret your results in the context of the situation. Is the company lying? Are you sure? What sampling method was used? Is there a better way to sample this population?
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.
Mathcorp has 35,000 employees and claims that the average salary is $50,000. You are an investigative journalist who wants to know what the average salary actually is for a Mathcorp employee, but the company does not publically post their budget or salaries.
You post a question on popular online message board Read It, and 57 employees respond. However, you can only verify 36 of the results after calling Mathcorp and speaking with the employee directly on the phone. You decide to use these 36 people as your sample.
After collecting the results into a spreadsheet, you run the calculation and find out that the
question
- Run a full hypothesis test with a significance level of 5%.
- Interpret your results in the context of the situation. Is the company lying? Are you sure?
- What sampling method was used? Is there a better way to sample this population?
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