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# Hypothesis Testing & Normal Probability

A researcher is studying the wait time of patients entering the emergency room for a particular hospital in Miami. The researcher obtains the weight time (in minutes) for a sample of 15 individuals. The wait times for the 15 individuals are given in the table below:

125 91 128 81 134
135 123 86 82 121
95 90 86 106 107

Based on this data, answer the following questions.

2a. Compute the sample mean and sample standard deviation for this data.

2b. In words, explain what the obtained value of the standard deviation means.

2c. The national mandate for mean waiting times in emergency rooms is 90 minutes (one and a half hour). Using this data, test the null hypothesis that the mean waiting time for this hospital equals the mandated value of 90 minutes. Use a Type I error rate of .05.

2d. A hospital administrator claims that the obtained sample data in the table above is not really representative of the true wait times. This administrator claims that they were unexpected short-staffed while the data were collected, and thus the obtained sample mean is biased. The administrator also claims that they have kept careful records of wait times through their computer system and know that the actual mean wait time for the past year has been 92 minutes with a standard deviation of 20 (that is, the known population mean and standard deviation of wait time for this emergency room is 92 and 20). Based on this information, what is the probability that a sample of 15 individuals will have a mean wait time equal to or greater than that observed for the 15 individuals in the table given above?

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Statistics

A researcher is studying the wait time of patients entering the emergency room for a particular hospital in Miami. The researcher obtains the weight time (in minutes) for a sample of 15 individuals. The wait times for the 15 individuals are given in the table below:

125 91 128 81 134
135 123 86 82 121
95 90 86 106 107

Based on this data, answer the following questions.
2a. Compute the sample mean and sample standard deviation for this data.
X X - X̅ (X - X̅)^2
125 19 361
91 -15 225
128 22 484
81 -25 625
134 28 784
135 29 841
123 17 289
86 -20 400
82 -24 576
121 15 225
95 -11 121
90 -16 256
86 -20 400
106 0 0
107 1 1
1590 5588

Sample Mean = = 106
Sample standard deviation = = 19.97855994
2b. In words, explain what the obtained value of the standard deviation means.
The standard deviation is the square root of variance, a measure of the degree of ...

#### Solution Summary

The solution provides step by step method for the calculation of testing of hypothesis and normal probability. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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