Question

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The National Institute of Standards and Technology (NIST) offers Standard Reference Materials to aid in the calibration of measurement instruments and verify the accuracy of measurements. Suppose a medical researcher wants to verify that the distances he measures with his computed tomography machine are not too large, so he orders a Dimensional Standard for Medical Computed Tomography from NIST. This standard consists of 18 plastic balls held in place by a plastic support structure. The certified distance between the balls numbered 1 and 3 is 20.15 mm, and NIST determines that measurement errors are normally distributed with a standard deviation of 0.05 mm. Upon receiving the Standard Reference Material, the researcher measured the distance between balls 1 and 3 six times. Take these six measurements to be a simple random sample of all measurements made on this device under carefully controlled conditions. The researcher then calculated the summary statistics, where p is the mean distance between balls 1 and 3, as measured by his computed tomography machine. Test of u = 20.15 vs u > 20.15 The assumed standard deviation = 0.05 Sample size Sample mean Standard error SE 20.17 0.02041 Complete the analysis by calculating the value of the one-sample z-statistic, the p-value, and making the decision. First, calculate z to at least two decimal places. Use software or a table of standard normal critical values to determine the P-value. Give your answer precise to at least four decimal places.

Answer 1

Test statistic = z

= ($\bar x$ - $\mu$ ) / $\sigma$    / $\sqrt$ n

= (20.17 - 20.15) / 0.02041

Test statistic = 0.98

P(z > 0.98) = 0.1635

P-value = 0.1635