A simple random sample of 100 postal employees is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago. The sample mean was ¯ x = 7 years with a standard deviation of s = 2 years. Assume the distribution of the time the employees have worked for the postal service is approximatelyNormal. The hypotheses being tested areH0 : μ = 7.5,Ha : μ , 7.5. A one-sample t test will be used. (a) What are the appropriate degrees of freedom for this test? (b) What is the P-value for the one-sample t test? (c) What is a 95% confidence interval for m, the population mean time the postal service employees have s
A simple random sample of 100 postal employees is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago. The sample mean was ¯ x = 7 years with a standard deviation of s = 2 years. Assume the distribution of the time the employees have worked for the postal service is approximatelyNormal. The hypotheses being tested areH0 : μ = 7.5,Ha : μ , 7.5. A one-sample t test will be used. (a) What are the appropriate degrees of freedom for this test? (b) What is the P-value for the one-sample t test? (c) What is a 95% confidence interval for m, the population mean time the postal service employees have s
A simple random sample of 100 postal employees is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago. The sample mean was ¯ x = 7 years with a standard deviation of s = 2 years. Assume the distribution of the time the employees have worked for the postal service is approximatelyNormal. The hypotheses being tested areH0 : μ = 7.5,Ha : μ , 7.5. A one-sample t test will be used. (a) What are the appropriate degrees of freedom for this test? (b) What is the P-value for the one-sample t test? (c) What is a 95% confidence interval for m, the population mean time the postal service employees have s
A simple random sample of 100 postal employees is used to test if the average time postal employees have worked for the postal service has changed from the value of 7.5 years recorded 20 years ago. The sample mean was ¯ x = 7 years with a standard deviation of s = 2 years. Assume the distribution of the time the employees have worked for the postal service is approximatelyNormal. The hypotheses being tested areH0 : μ = 7.5,Ha : μ , 7.5. A one-sample t test will be used. (a) What are the appropriate degrees of freedom for this test? (b) What is the P-value for the one-sample t test? (c) What is a 95% confidence interval for m, the population mean time the postal service employees have spent with the postal service? (d) Suppose the mean and standard deviation obtained were based on a sample of size n = 25 postal workers rather than 100. What do we know about the value of the P-value? i. It would be larger. ii. It would be smaller. iii. It would be unchanged because the difference between and the hypothesized value m = 7.5 is unchanged. iv. Itwould be unchanged because the variabilitymeasured by the standard deviation stays the same.
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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