The population mean waiting time to check out of a supermarket has been 4 minutes. Recently, in an effort the waiting time, the supermarket has experimented with a system in which infracted cameras use body hear and in-store software to determine how many lanes should be opened. A sample of 100 customers was selected, and their mean waiting time to check out was 3.10 minutes, with a sample standard deviation of 2.5 minutes. a. At the 0.05 level of significance, using the critical value approach to hypothesis testing, is there evidence that the population mean waiting time to check out is less than 4 minutes? b. At the 0.05 level of significance, using the p -value approach to hypothesis testing, is there evidence that the population mean waiting time to check out is less than 4 minutes? c. Interpret the meaning of the p -value in this problem. d. Compare your conclusions in (a) and (b).
The population mean waiting time to check out of a supermarket has been 4 minutes. Recently, in an effort the waiting time, the supermarket has experimented with a system in which infracted cameras use body hear and in-store software to determine how many lanes should be opened. A sample of 100 customers was selected, and their mean waiting time to check out was 3.10 minutes, with a sample standard deviation of 2.5 minutes. a. At the 0.05 level of significance, using the critical value approach to hypothesis testing, is there evidence that the population mean waiting time to check out is less than 4 minutes? b. At the 0.05 level of significance, using the p -value approach to hypothesis testing, is there evidence that the population mean waiting time to check out is less than 4 minutes? c. Interpret the meaning of the p -value in this problem. d. Compare your conclusions in (a) and (b).
Solution Summary: The author explains how to test whether there is evidence that the population mean waiting time to checkout is less than 4 minutes using the critical value approach.
The population mean waiting time to check out of a supermarket has been 4 minutes. Recently, in an effort the waiting time, the supermarket has experimented with a system in which infracted cameras use body hear and in-store software to determine how many lanes should be opened. A sample of 100 customers was selected, and their mean waiting time to check out was 3.10 minutes, with a sample standard deviation of 2.5 minutes.
a. At the 0.05 level of significance, using the critical value approach to hypothesis testing, is there evidence that the population mean waiting time to check out is less than 4 minutes?
b. At the 0.05 level of significance, using the p-value approach to hypothesis testing, is there evidence that the population mean waiting time to check out is less than 4 minutes?
c. Interpret the meaning of the p-value in this problem.
d. Compare your conclusions in (a) and (b).
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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