Laser can provide a highly accurate measurement of small movements. To determine

Question

Laser can provide a highly accurate measurement of small movements. To determine the accuracy of such laser, it was used to take 169 measurement of a known quantity. The sample mean error was 25 urn with a standard deviation of 60 |im. The laser is properly calibrated if the mean error is mu=0. Do you believe it the laser is out of calibration? (Make a Hypothesis test, define H_0 and H_1, clearly, calculate P-value and then draw the conclusion. Express the inference using 1% level of significance)

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu = 0 Vs H1 : mu 0

where mu is population mean.

number of measturements (n) = 169

sample mean error (Xbar) = 25

standard deviatio(sd) = 60

Alpha = 1% = 0.01

Here sample size is large so we use z-test for one sample.

This we can done using TI-83 calculator.

Steps :

STAT --> TESTS --> 1: Z-Test --> ENTER --> Highlight on Stats --> Input all the values mu0, sigma, Xbar and n --> select alternative "mu0" --> ENTER --> Calculate --> ENTER

Output is :

Test statistic Z = 5.4167

P-value = 0.0000

P-value < alpha

Reject H0 at 1% level of significance.

Conclusion : There is sufficient evidence to say that the laser is out of calibration.

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