A pharmaceutical company claims that the mean for an active ingredient in a new

Question

A pharmaceutical company claims that the mean for an active ingredient in a new drug is 1.5mg, with a standard deviation of 0.2mg. The company is investigating this claim by testing a sample of n=49 using the hypothesis H0: = 1.5 versus H1 :   > 1.5. The sample mean, X was found to be 1.58

At the 95% level of significance what’s the probability of getting a Type I error?

At the 95% level of significance what’s the probability of getting a Type II error if the true mean for the active ingredient is 1.6mg? What is the power test?

A pharmaceutical company claims that the mean for an active ingredient in a new drug is 1.5mg, with a standard deviation of 0.2mg. The company is investigating this claim by testing a sample of n=49 using the hypothesis H0:   U= 1.5 versus H1 : U > 1.5. The sample mean, X was found to be 1.58

At the 95% level of significance what’s the probability of getting a Type I error?

At the 95% level of significance what’s the probability of getting a Type II error if the true mean for the active ingredient is 1.6mg? What is the power test?

Explanation / Answer

The claims of a pharmaceutical companyis that the mean for an active ingredient in a new drug is 1.5mg,

the hypothesis H0: = 1.5 versus H1 :   > 1.5

One-Sample Z

Test of mu = 1.5 vs > 1.5
The assumed standard deviation = 0.2

N Mean SE Mean 95% Lower Bound Z P
49 1.5800 0.0286 1.5330 2.80 0.003

therefore type I error is probability of reject Ho when Ho is true = 0.003

Type II error is probability of accept Ho when H1 is true = 0.242

and power of the test is 1 - Type II error = 1 - 0.242 = 0.758

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