Faculty of Engineering, Architecture and Science
Department of Mechanical and Industrial Engineering
Program: Mechanical Engineering/Industrial Engineering
Experimental Design and Quality Assurance
Dr. Sharareh Taghipour
Lab/Tutorial Report NO.
Inference for Two Samples
October 10, 2014
October 10, 2014
Parvin M Ghalehtaki
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The main purpose of the lab is to emphasise the use of measurements techniques through practice experience, to conduct an analysis on statistical inference, evaluating the difference between two sample means using a hypothesis test. A statistical hypothesis is a statement about the values of the parameter of a probability distribution. A hypothesis test is used to make inferences about one or more populations when sample data are available. The two-sample t-test is one of many procedures available for hypothesis testing. This statistical analysis is to be done with the data collected from the measurements done at the laboratory. It was used a two-sample t-test with continuous data from two independent random samples. Basic length and weight measurements on a sample of ten rods from uncut white and yellow drawer were carried out using a micrometer. The micrometer is a precision measuring instrument, used by engineers. In the hands of a skilled operator, the precision micrometer is the most accurate hand-held tool available. When close measurements are necessary, the micrometer is the ideal tool for the job because measurement and reading are on the same axis and the anvil end is supported by a strong frame. Method
To begin the experiment, a drawer containing a sample of 10 cylinders was obtained. The cylinders were located between the anvil and spindle of the micrometer, and the thimble was rotated to slowly close the micrometer around the cylinders. This method was used to measure the lengths of each cylinder. Once the length measurements were completed, a digital scale was used to measure the weight of each cylinder. The length and weight values for each cylinder (numbered from 1-10) were tabulated and the mean of both sets of values will be used to carry out the analysis that follows. Materials:
10 cylinder rods (uncut white)
Figure - Diagram of an External Micrometer
1.1 Keep the micrometer in stable room temperature before starting the measuring process. 1.2 Hold the micrometer from its heat isolation plate.
1.3 Rotate the ratchet anticlockwise allowing sufficient space between the anvil and the spindle to accommodate the object to be measured. 1.4 Place the object to be measured between the anvil and the spindle. 1.5 Spin the ratchet clockwise until the spindle just meets the object. 1.6 Keep spinning the ratchet gently until 3 clicks are heard. 1.7 Check that both the anvil and the spindle are touching the object evenly. 1.8 Set the lock nut while the micrometer is still on the object. 1.9 Remove the object from the micrometer.
1.10 Read off the value from the barrel scale to obtain reading to the nearest half millimetre. 1.11 Read off the value from the thimble scale that is parallel with the reference line of the barrel scale. 1.12 Add both values obtained from 1.9 and 1.10 to obtain the total measurement reading. Part 2:
2.1 Mass each of the 10 cylindrical rod pieces, recording each entry. 2.2 Find the average value for the mass and perform the calculation analysis. Calculations & Analysis
Data Gathering (Measurements):
Given Sample Information:
The first step of a hypothesis test is to determine the null and alternative hypotheses. The null hypothesis usually specifies that a parameter equals a specific value. The test assumes that the data come from normally distributed populations and uses the sample standard deviations to estimate σ for each population.