Suppose a new Director of Health Services for a district claims that she will reduce the average speed of emergency response to less than 30 minutes, which is thought to be the average response time with the current Director. There are no past records; so the actual standard deviation of such response times cannot be determined. Thanks to this promise, careful records are now kept. The response times for the first month are 26, 30, 28, 29, 25, 28, 32, 35, 24, and 23 minutes. Using the .05 level of significance, did she keep her promise? Explain your answer.
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 a new Director of Health Services for a district claims that she will reduce the average speed of emergency response to less than 30 minutes, which is thought to be the average response time with the current Director. There are no past records; so the actual standard deviation of such response times cannot be determined. Thanks to this promise, careful records are now kept. The response times for the first month are 26, 30, 28, 29, 25, 28, 32, 35, 24, and 23 minutes. Using the .05 level of significance, did she keep her promise? Explain your answer.
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