10) Making sure that the scales used by businesses in the United States are accurate is theresponsibility of the National Institute for Standards and Technology (NIST) inWashington, D.C. Suppose that NIST technicians are testing a scale by using a weightknown to weigh exactly 1000 grams. The population standard deviation for scalereading is known to be 3.1. They weigh this weight on the scale 45 times and read theresult each time. The 45 scale readings have a sample mean of 999.4 grams. The scale isout of calibration if the mean scale reading differs from 1000 grams. The technicianswant to perform a hypothesis test to determine whether the scale is out of calibration.Use the 0.01 level of significance and the P-value method.
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Step 1: State hypotheses - Null hypothesis H0: μ = 1000 (scale is in calibration) - Alternative hypothesis Ha: μ ≠ 1000 (scale is out of calibration) Show more…
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Madhur L.
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 = 3.0. They weigh this weight on the scale 54 times and read the result each time. The 54 scale readings have a sample mean of x = 1001.0 grams. The calibration point is set too high if the mean scale reading is greater than 1000 grams. The technicians want to perform a hypothesis test to determine whether the calibration point is set too high. Use the α = 0.05 level of significance and the P-value method with the TI-84 calculator.
Ariana N.
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 = 2.0. They weigh this weight on the scale 47 times and read the result each time. The 47 scale readings have a sample mean of x̄ = 999.1 grams. The calibration point is set too low if the mean scale reading is less than 1000 grams. The technicians want to perform a hypothesis test to determine whether the calibration point is set too low. Use the α = 0.01 level of significance and the P-value method with the TI-84 calculator. State the appropriate null and alternate hypotheses. H0: H1: This hypothesis test is a test.
Adi S.
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