An ACME Bearings manager wants to compare the average ball bearing sizes from two different machines. She suspects the mean diameter for bearings from machine 2 exceeds that of bearings from machine 1. She takes two independent, random samples of size 50, one from each machine. The mean and standard deviation of bearings taken from machine 1 are 3.302 mm and 0.051 mm. The mean and standard deviation of bearings taken from machine 2 are 3.355 mm and 0.050 mm. Run a hypothesis test consistent with her suspicions. Be sure to check all necessary assumptions;
An ACME Bearings manager wants to compare the average ball bearing sizes from two different machines. She suspects the mean diameter for bearings from machine 2 exceeds that of bearings from machine 1. She takes two independent, random samples of size 50, one from each machine. The mean and standard deviation of bearings taken from machine 1 are 3.302 mm and 0.051 mm. The mean and standard deviation of bearings taken from machine 2 are 3.355 mm and 0.050 mm. Run a hypothesis test consistent with her suspicions. Be sure to check all necessary assumptions;
An ACME Bearings manager wants to compare the average ball bearing sizes from two different machines. She suspects the mean diameter for bearings from machine 2 exceeds that of bearings from machine 1. She takes two independent, random samples of size 50, one from each machine. The mean and standard deviation of bearings taken from machine 1 are 3.302 mm and 0.051 mm. The mean and standard deviation of bearings taken from machine 2 are 3.355 mm and 0.050 mm. Run a hypothesis test consistent with her suspicions. Be sure to check all necessary assumptions;
An ACME Bearings manager wants to compare the average ball bearing sizes from two different machines. She suspects the mean diameter for bearings from machine 2 exceeds that of bearings from machine 1. She takes two independent, random samples of size 50, one from each machine. The mean and standard deviation of bearings taken from machine 1 are 3.302 mm and 0.051 mm. The mean and standard deviation of bearings taken from machine 2 are 3.355 mm and 0.050 mm. Run a hypothesis test consistent with her suspicions. Be sure to
check all necessary assumptions;
state the null and alternative hypotheses;
decide whether or not to pool and explain why;
calculate the test statistic and p-value;
state your conclusion in a complete sentence based on the p-value.
Transcribed Image Text:3. An ACME Bearings manager wants to compare the average ball bearing
sizes from two different machines. She suspects the mean diameter for
bearings from machine 2 exceeds that of bearings from machine 1. She
takes two independent, random samples of size 50, one from each
machine. The mean and standard deviation of bearings taken from
machine 1 are 3.302 mm and 0.051 mm. The mean and standard deviation
of bearings taken from machine 2 are 3.355 mm and 0.050 mm. Run a
hypothesis test consistent with her suspicions. Be sure to
a. check all necessary assumptions;
b. state the null and alternative hypotheses;
c. decide whether or not to pool and explain why;
d. calculate the test statistic and p-value;
e. state your conclusion in a complete sentence based on the p-value.
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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