1.5 Problem 5 (8 points) sample of 16 radon detectors of a certain type was sele

Question

1.5 Problem 5 (8 points) sample of 16 radon detectors of a certain type was selected, and each was exposed to 100 pCi/L of radon. The resulting readings were as follows: n = 16,2 = 97.075, 6.1095. a. Does this data suggest that the population mean reading under these conditions is different from 100? State and test the appropriate hypotheses using (al) -0.10, (a2) 0.05, (a) =0.01. b. Does this data suggest that the population mean reading under these conditions is less than 100? State and test the appropriate hypotheses using (b1) 0.10, (62) -005, (b) =0.01.

Explanation / Answer

a)
Hypothesis:

H0 : mu = 100
Ha: munot equal to 100

Test statistics:

x = 97.075 , s = 6.1095 , n= 16

t = ( x - mu) / ( s/sqrt(n))
= ( 97.075 - 100)/(6.1095/sqrt(16))
= -1.9151

P value is calculated using t = -1.9151 with df = 15
a1) at 0.1 significance level
p value = .0747
we reject the null hypothesis.

a2) at 0.05 significance level
p value = .0747
we do not reject the null hypothesis.

a3) at 0.01 significance level
p value = .0747
we do not reject the null hypothesis.

b)

Hypothesis:

H0 : mu = 100
Ha : mu < 100

Test statistics:

x = 97.075 , s = 6.1095 , n= 16

t = ( x - mu) / ( s/sqrt(n))
= ( 97.075 - 100)/(6.1095/sqrt(16))
= -1.9151

P value is calculated using t = -1.9151 with df = 15
a1) at 0.1 significance level
p value = .0374
we reject the null hypothesis.

a2) at 0.05 significance level
p value = .0374
we reject the null hypothesis.

a3) at 0.01 significance level
p value = .0374
we do not reject the null hypothesis.

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