A spectrophotometer used for measuring CO concentration (parts per million by vo
ID: 3153652 • Letter: A
Question
A spectrophotometer used for measuring CO concentration (parts per million by volume) is checked for accuracy by taking readings on a manufactured gas (called span gas) in which the CO concentration is very precisely controlled at 70 ppm. If the readings suggest that the spectrophotometer is not working properly, it will have to be recalibrated. Assume that if it is properly calibrated, measured concentration for span gas samples is normally distributed. On the basis of six readings below, is recalibration necessary?
85 77 82 68 72 69
Carry out a test of the relevant hypotheses using alpha = .05.
a) Use the critical value approach
b) Use the p-value approach
Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u = 70
Ha: u =/ 70
As we can see, this is a two tailed test.
Thus, getting the critical t,
df = n - 1 = 5
tcrit = +/- 2.570581836
Getting the test statistic, as
X = sample mean = 75.5
uo = hypothesized mean = 70
n = sample size = 6
s = standard deviation = 7.007139217
Thus, t = (X - uo) * sqrt(n) / s = 1.922638208
As |t| < 2.571, we FAIL TO REJECT HO.
Hence, there is no significant evidence that the true mean is not 70 ppm. Recalibration is not necessary. [CONCLUSION]
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b)
Also, the p value is, as this is two tailed,
p = 0.112547339
As P > 0.05, we FAIL TO REJECT HO.
Hence, there is no significant evidence that the true mean is not 70 ppm. Recalibration is not necessary. [CONCLUSION]
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