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 =σ3.2. They weigh this weight on the scale 52 times and read the result each time. The 52 scale readings have a sample mean of =x1000.6 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 =α0.01 level of significance and the P-value method with Excel. a) Compute the value of the test statistic. Round the answer to at least two decimal places. Z=? b) State the appropriate null and alternate hypotheses (c) State a conclusion. Use the α=0.01 level of significance.
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 =σ3.2. They weigh this weight on the scale 52 times and read the result each time. The 52 scale readings have a sample mean of =x1000.6 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 =α0.01 level of significance and the P-value method with Excel. a) Compute the value of the test statistic. Round the answer to at least two decimal places. Z=? b) State the appropriate null and alternate hypotheses (c) State a conclusion. Use the α=0.01 level of significance.
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 =σ3.2. They weigh this weight on the scale 52 times and read the result each time. The 52 scale readings have a sample mean of =x1000.6 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 =α0.01 level of significance and the P-value method with Excel. a) Compute the value of the test statistic. Round the answer to at least two decimal places. Z=? b) State the appropriate null and alternate hypotheses (c) State a conclusion. Use the α=0.01 level of significance.
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 =σ3.2. They weigh this weight on the scale 52 times and read the result each time. The 52 scale readings have a sample mean of =x1000.6 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 =α0.01 level of significance and the P-value method with Excel.
a) Compute the value of the test statistic. Round the answer to at least two decimal places. Z=?
b) State the appropriate null and alternate hypotheses
(c) State a conclusion. Use the α=0.01 level of significance.
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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