Respuesta :
The probability of Type I error is the likelihood of finding a mean outside
the safe zone for the 4 pools.
- The probability that the inspector will make a Type I error is 0.0026
What is a Type I error and what is the probability that it will occur?
In hypothesis testing, a Type I error is the error of rejecting a true null
hypothesis.
From a similar question, the possible parameters are;
The safe pH levels for swimming pools is between 7.2 and 7.8
The standard deviation is 0.2
The probability that the pH is within the safe zone is found as follows;
[tex]The \ z-score, \ Z = \mathbf{\dfrac{\overline x - \mu}{\dfrac{\sigma}{n} }}[/tex]
Which gives;
[tex]\mathbf{P \left(\dfrac{7.2 - 7.5}{\dfrac{0.2}{\sqrt{4} } } < \dfrac{\overline x - \mu}{\sigma} < \dfrac{7.8 - 7.5}{\dfrac{0.2}{\sqrt{4} }} \right)} = P(-3 < Z < 3)[/tex]
P(-3 < Z < 3) = P(Z < 3) - P(Z > -3) = P(Z < 3) - (1 - P(Z < 3))
P(Z < 3) - (1 - P(Z < 3) = 2·P(Z < 3) - 1
2·P(Z < 3) - 1 = 2 × 0.9987 - 1 = 0.9974
The probability that the swimming pool is not safe = 1 - (2·P(Z < 3) - 1)
1 - (2·P(Z < 3) - 1) = 1 - 0.9974 = 0.0026
Which gives;
- The probability that the mean will be seen as not in the safe zone and therefore not 7.5 is 0.0026 and the probability that the inspector will make a Type I error is 0.0026
Learn more about hypothesis testing here:
https://brainly.com/question/23082833
