The physician-recommended dosage of a new medication is 14 mg. Actual administer

Question

The physician-recommended dosage of a new medication is 14 mg. Actual administered doses vary slightly from dose to dose and are Normally distributed with mean. A representative of a medical review board wishes to see if there is any evidence that the mean dosage is more than recommended and so intends to test the hypotheses given below. H0 : = 14, Ha : > 14 To do this, he selects 16 doses at random and determines the weight of each. He finds the sample mean to be = 14.12 mg and the sample standard deviation to be s = 0.24 mg. Based on these data, test the hypotheses using significance level 0.05.

I understand most of the problem except where the =2 part comes from in the 14.12-14/0.24*sqrt 16=2 and how the P value= 0.0320 and how the mean dosage is greater than 14 mg. If that could be explained, that would be great. Thanks!

Explanation / Answer

There is given all data like ,

Hypothesis is given:

H0 : mean = 14

Ha : mean >14

There is mentioned that evidence that the mean dosage is more than recommended so we took alternative hypothesis is greater.

Test statistic:

x = 14.12 , s = 0.24 , n = 16

So, we apply the normal distribution formula,

t = ( x - mean) / (s/sqrt(n))

= ( 14.12 - 14) / ( 0.24 / sqrt(16))

= 2

Now,w e need to find p value using t = 2 and df = 16-1 = 15

p value = 0.032

So, p value is less than 0.05 so, we reject the null hypothesis

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