Probabilities of Type I and Type II Error Homework Help

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Check out Statistics with Probabilities of Type I and Type II Error Homework Help

Before we start you need to know about Type I and Type II errors. What are they? According to statistical hypothesis testing, Type I error symbolizes the incorrect rejection of a true null hypothesis; whereas type II error means the failure to reject a wrongnull hypothesis. To be very precise, type I error fails to find an effect that is not absent. You can get full support any time for probabilities of type I and type II error assignment help.

Probabilities of type I error:

It means the level of significance of the test of hypothesis. It is recognized by α (Alpha).

Example: Say, for a medical test (may be a blood sugar, cholesterol etc.) for men, the lab readings are following a normal distribution with the mean being 180 and SD (standard deviation) being 20. Men with readings over 225 will be considered as not healthy, then what will be the probability of Type I error in this case? Here, the value of Z will (225 – 180) divided by SD, i.e., 45 / 20 = 2.25. The corresponding tail area is going to be 0.0122 and this is the probability of Type I error.

If the lab output of healthy men follows a normal distribution while the mean is 180 and SD is 20, at what level, the men should be diagnosed as unhealthy if the probability of a Type I error is to be 2%? This can be solved as 2% in the tail area will correspond to a Z-Score of 2.05. Hence, 2.05 X 20 = 41. And the level needs to 180 + 41 = 221.

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Probabilities of type II error:

Following the above example, if we consider the mean as 300 with a SD of 30, but only men with values over 225 are diagnosed as predisposed to health hazard, what will be the probability of a type II error. Here, Z will be [(300 – 225)=] 75/30 = 2.5. This corresponds to a tail area of 0.0062 which is the probability of a Type II error.

If men predisposed to the health hazard have a mean figure of 300 and SD value equaling 30, above what level the men should be diagnosed as prone to diseases if the probability of the type II error has to be 1%? Here again, 1% corresponds to the tail area for Z-Score of -2.33. So, -2.33 multiplied by 30 (SD) is -70. So, the value will be 300 – 70 = 230.

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