Question

Calibrating a scale: Making sure that the scales used by businesses in the United States are accurate is the responsibility of the National Institute for Standards and Technology (NIST) in Washington, D.C. Suppose that NIST technicians are testing a scale by using a weight known to weigh exactly 1000 grams. The standard deviation for scale reading is known to be σ=3.1. They weigh this weight on the scale 45 times and read the result each time. The 45 scale readings have a sample mean of x=999.4 grams. The scale is out of calibration if the mean scale reading differs from 1000 grams. The technicians want to perform a hypothesis test to determine whether the scale is out of calibration. Use the α=0.01 level of significance and the P-value method with the table.
1) State the appropriate null and alternate hypotheses.

H0:
H1:

This hypothesis test is a two tailed, right or left test?

2) Compute the value of the test statistic. Round the answer to at least two decimal places.

3)Find the P-value. Round the answer to at least four decimal places.

4) Determine whether to reject H0.

reject or do not reject  the null hypothesis H0?

5) State a conclusion.

There is or is not enough evidence to conclude that the calibration point Is set too high, calibration point is set too low or scale is out of calibration

Answer 1

(1) The Hypothesis

H0: = 1000

Ha: 1000

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(2) The Test Statistic:

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(3) The p Value: The p value (2 Tail) for Z = -1.30, is; p value = 0.1936

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(4) Since p value is > , Do not reject the null hypothesis, H0.

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(5) There is not enough evidence to conclude that the calibration point is out of calibration.

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