Question

Prob Hospital workers who are routinely involved administrative radioactive tracer to patients are subject to a radiation exposure emanating from skin of the patient. In an experiment to asses the amount of this, radiation levels were measured at a distance of 50 cm from 28 patients who had been injected with a radioactive tracer, and a sample mean of 5.145 and sample std. -0.7524 are obtained Can we be 95% confident that the average radiation level at a 50 cm, distance from patient is no more than about 5.5?

Answer 1

Answer)

Null hypothesis Ho : u <= 5.5

Alternate hypothesis Ha : u > 5.5

Given info

N = 28

Mean = 5.145

S.d = 0.7524

As the population s.d is unknown here we will use t distribution to conduct the test

Degrees of freedom is = n-1 = 27

For 27 dof and 95% confidence level

Critical value t from t table is 2.048

Margin of error (MOE) = t*s.d/√n = 2.048*0.7524/√28 = 0.29175

Interval is given by

(Mean - MOE, Mean + MOE)

[4.85325, 5.43675].

As the interval do not contain 5.5

We reject the null hypothesis

So we do not have enough evidence to support the claim.that mean is no more than 5.5