Question

Biostatistics

Null and alternative hypotheses, t-tests, and confidence limits

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2. (3 points) The Medassist company has developed a new cholesterol lowering drug. The drug comes in pills that claim to contain 25 mg of the drug. From this sample of pills, determine (using an alpha of 0.05) if the medication is properly manufactured (that is: does it contain 25 mg per pill, is the medicine content equal to 25 mg?). Show your null and alternative hypotheses and perform the appropriate test.

Drug amounts: 24.1 24.4 24.3 24.9 24.1 26.2 25.1 24.7 24.4 25.0 24.7 25.1 25.3 25.5 25.5

Answer 1

Ans:

n=15

sample mean=24.887

standard deviation=0.590

Test statistic:

t=(24.887-25)/(0.59/SQRT(15))

t=-0.744

df=15-1=14

p-value=tdist(0.744,14,2)=0.4692

As,p-value>0.05,we fail to reject the null hypothesis.

There is not sufficient evidence to conclude that medicine content equal is different from 25 mg.

critical t value=tinv(0.05,14)=2.145

95% confidence interval for mean

=24.887+/-2.145*(0.590/sqrt(15))

=24.887+/-0.327

=(24.560, 25.214)

As,above confidence interval includes 25 within its limits,so medicine content is not different from 25 mg.