woman is told that the grades on a standardized statistics test are normally distributed with a mean of 78 and a standard deviation of 5. Prof. Gersch wants to see whether the mean of all the tests is indeed really 78. He collects a random sample of 25 tests, finds the sample mean is 79 and thus constructs a 95% CI from 77 to 81. Then we can say that: a. It is 95% probable that the population mean falls into this range b. 95% of all values for the population mean of all tests fall into this range c. 95% of all possible sample average values fall into this range d. 95% of all test scores (ie, x values) fall into this range e. 95% of all similarly constructed intervals will contain our sample mean f. 95% of all similarly constructed intervals will contain the population mean of all the tests
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.
woman is told that the grades on a standardized statistics test are
Prof. Gersch wants to see whether the mean of all the tests is indeed really 78.
He collects a random sample of 25 tests, finds the sample mean is 79 and thus constructs a 95% CI from 77 to 81.
Then we can say that:
| a. |
It is 95% probable that the population mean falls into this
|
|
| b. |
95% of all values for the population mean of all tests fall into this range
|
|
| c. |
95% of all possible sample average values fall into this range
|
|
| d. |
95% of all test scores (ie, x values) fall into this range
|
|
| e. |
95% of all similarly constructed intervals will contain our sample mean
|
|
| f. |
95% of all similarly constructed intervals will contain the population mean of all the tests
|
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