Lasers can provide highly accurate measurements of small movements. To determine
ID: 3315578 • Letter: L
Question
Lasers can provide highly accurate measurements of small movements. To determine the accuracy of such a laser, it was used to take 100 measurements of a known quantity. The urement error was 25 um. Assume the population standard deviation of the measurement errors is 60 um. The laser is properly calibrated if the mean measurement sample mean meas error is 0. Is there evidence that the laser is not calibrated correctly? Use = .01. a. Specify the competing hypotheses to test whether the laser is properly calibrated. Define as the population mean of the laser measurement errors of a known quantity. M: 100 b. Is this Z test or T test? if it is T test, specify its degrees of freedom c Calculate the value of the test statistio d. Using the p-value approach, test the hypothesis in part a. pl zt. 1667)valye,0000 309 The lase, n out of cd:bction e. Repeat the hypothesis test in part d. using the critical value approach.Explanation / Answer
a. Below are the null and alternate hypothesis
H0: mu = 0
H1: mu not equals to 0
b. As population std. dev. is given and sample size is greater than 30, this is z-test.
c.
n = 100, xbar = 25, s = 60
Test statistics, z = (25 - 0)/(60/sqrt(100)) = 4.1667
d.
p-value = 0.000031
As p-value is less than the significance level of 0.05, we reject the null hypothesis.
There are significant evidence to conclude that the laser is out of calibration.
e.
Critical values for 0.05 significance level are +/- 1.96 for two tailed test.
Area to the right of 1.96 and left of -1.96 is rejection region
As the calculated test statitstics falls in the rejection region, we reject the null hypothesis.
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