4.1 Small Sample Statistics Follow the steps given below to determine the size of wood blocks using a caliper. 1. Random

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4.1 Small Sample Statistics Follow the steps given below to determine the size of wood blocks using a caliper. 1. Randomly take 15 pieces of wooden block with a nominal width of 57.5 mm. 2. Measure the width of block using calipers and record your measurements in Table 2.2. 3. Calculate sample arithmetic average, deviation, and standard deviation. Use MS Excel to record the measurements and make the computations. 58.०५ 0.17 Table 2.2. Width measurements of wood blocks. Deviation (d) Width of Block(w) [mm] Deviation Squared (d) d=x- 0.07 0-0049 57086 0.0121 57-07 -0.9 0.81 53.00 0.03 0-0009 58.14 0-0289 58.1 - 0-8169 57.92 0.05 0-00 25 58.06 0.09 0.0081 58.22 0-0625 58.22 0.25 O *0625 58.04 0.07 0-6049 58.04 0.07 0.0049 57.82 0-0225 58.14 0.17 0-0289 57.92 -0.05 O-0025 Total Width Σw: 1869.59 Total Deviation Squared Ed?: 1.673 Mean Estimate 869.59 Standard Deviation 11.073 w=w/N: 15 S = Ed"/(N-1) = 0-28 15.1 0.25 -0.15 = 57.97
Please answer the following questions: ones. read to a resolution of cool mm or 0.0005 but accuras may not be better then abait 10-02 mmoro.coin for 150 mm (6in) 1. What is the resolution of calipers? Calipers may Calipers and worse for longer 2. What is degree of freedom of the measurement? Degrecol freedom are commonly discussed in relation to various froms of hypothesis testing in statistics, such as a chisquare 3. Calculate the 95% confidence interval for the true mean (u). Please show all your work. =ł + 196 = 57.97 +1.96 0.28 57.97 +1.96 X 0.28 15 3.87 - 57.97 to 142 (58.112, 57.828) 4. Calculate the experimental t-statistic. Please show all your work. Ň -w 5 = -0-04 0-285175 -0.94 0.28 - 3.87 -0.04 0-072 -0-556
5. Using hypothesis testing, determine whether the sample mean is not equal to the block population's true mean (+4.) with a confidence level of 95%. Please clearly indicate your choice of the null and alternate hypotheses, and show all your work. M 57. 6. Get the sample mean and standard deviation from another group. Using hypothesis testing, determine if there is a significant difference between the block widths of the two groups at a confidence level 95% using the t-test comparison.
5. Using hypothesis testing, determine whether the sample mean is not equal to the block population's true mean (+4.) with a confidence level of 95%. Please clearly indicate your choice of the null and alternate hypotheses, and show all your work. M 57. 6. Get the sample mean and standard deviation from another group. Using hypothesis testing, determine if there is a significant difference between the block widths of the two groups at a confidence level 95% using the t-test comparison.