(a) The article “Study on the Life Distribution of Microdrills" (Z. Yang, Y. Chen, andY. Yang, Journal of Engineering Manufacture, 2002:301–305) reports that in asample of 50 micro drills drilling a low-carbon alloy steel, the average lifetime(expressed as the number of holes drilled before failure) was 12.68 with a standard4deviation of 6.83. Construct a 95% confidence interval for the mean lifetime ofmicro drills under these conditions.(b) Based on a large sample of capacitors of a certain type, a 95% confidence intervalfor the mean capacitance, in µF, was computed to be (0.213, 0.241). Construct a90% confidence interval for the mean capacitance of this type of capacitor.(c) The article “An Automatic Visual System for Marble Tile Classification" (L.Carrino, W. Polini, and S. Turchetta, Journal of Engineering Manufacture,2002:1095–1108) describes a measure for the shade of marble tile in which theamount of light reflected by the tile is measured on a scale of 0–255. A perfectlyblack tile would reflect no light and measure 0, and a perfectly white tile wouldmeasure 255. A sample of nine Mezza Perla tiles were measured, with thefollowing results:204.999206.149202.102207.048203.496206.343203.496206.676205.831Construct a 95% confidence interval for the mean shade of Mezza Perla tile.

NOTE- AS PER COMPANY POLICY I HAVE CALCULATED FIRST MAIN QUESTION ONLY HERE GIVEN FOR AVG LIFETIME…

Answered: (a) The article “Study on the Life…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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2) An Izod impact test was performed on 19 specimens of PVC pipe, the standard deviation was 0.25. We wish to test the hypothesis that Ho: o 0.10 against H₁: >0.10. (a) State any necessary assumption about the underlying distribution of the data. (b) Calculate the test statistic value. (c) What is the critical value? Use a= 0.01 (d) Is it possible to reject Ho hypothesis at the 0.01 level of significance? Explain (e) What is the P-value?
The article “Predicting Profit Performance for Selecting Candidate International Construction Projects” (S. Han, D. Kim, and H. Kim, Journal of Construction Engineering and Management Science, 2007: 425–436) presents an analysis of the profit of inter- national construction projects. In a sample of 126 projects, the average profit margin (in percent) was 8.24 with a standard deviation of 16.33. A test is made of H0:μ≥10 versus H1:μ<10. Find the P-value.   Do you believe that it is plausible that the mean profit margin is at least 10%, or are you convinced that it is less than 10%? Explain your reasoning.
The breaking strengths of cables produced by a certain manufacturer have a mean, μ, of 1900 pounds, and a standard deviation of 55 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 80 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1912 pounds. Can we support, at the 0.05level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.) Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1 . H0: H1: (b) Determine the type of test statistic to use. ▼(Choose one) (c) Find the value of the test statistic. (Round…
1) Sampling Distribution for Sample Variances a) A cell phone manufacturer wants to advertise their new extended-life batteries. They believe the lifetimes are normally distributed with o = 1.15 hr. A test engineer takes a sample of 10 batteries and calculates a sample standard deviation of 1.3 hr. Can the manufacturer confidently advertise the standard deviation in the lifetime of their new batteries? Use critical values of X1.95 and X3.05 (a 90% window). i) Find the value of the test statistic for this sample and the two critical values. ii) 2 X0.95 = YES x² = Can the manufacturer confidently advertise the standard deviation in the lifetime of their new batteries? Circle YES or NO and briefly explain your answer. NO X0.05 =
8. 140 migrating pigeons were caught by a biologist for data collection. The mass of these pigeons is normally distributed with mean 0.9 kg and standard deviation of deviation 0.15 kg. a) Determine the percentile rank of a pigeon weighing 1kg. b) What proportions of pigeons have weight greater than 1.1 kg or less than 0.7 Kg 31
A sample of 12 concrete specimens from supplier A were tested for their compressive strength. The results gave an average of 85 MPa and a standard deviation of 4 MPa. From supplier B, 10 specimens were similarly tested and gave an average compressive strength of 81 MPa and a standard deviation of 5 MPa. (a) Using procedures of Hypothesis Testing, can we conclude at the 0.05 level of significance that the compressive strength of concrete from A exceeds that from B by more than 2 MPa? Assume the populations to be approximately normal with equal variances. (b) Is the assumption of equal variances in (a) justifiable at an a = 0.10?
7.1
Facebook: A study showed that two years ago, the mean time spent per visit to Facebook was 20.8 minutes, Assume the standard devlation is o= 8.0 minutes. Suppose that a simple random sample of 107 visits was selected this year and has a sample mean of x= 18.8 minutes. A social scientist is interested to know whether the mean time of Facebook visits has decreased. Use the a=0.10 level of significance and the critical value method with the table. (a) State the appropriate null and alternate hypotheses. (b) Compute the value of the test statistic. (c) State a conclusion. Use the a = 0.10 level of significance.
The breaking strengths of cables produced by a certain manufacturer have a mean, μ , of 1850 pounds, and a standard deviation of 50 pounds. It is claimed that an improvement in the manufacturing process has increased the mean breaking strength. To evaluate this claim, 100 newly manufactured cables are randomly chosen and tested, and their mean breaking strength is found to be 1864 pounds. Can we support, at the 0.1 level of significance, the claim that the mean breaking strength has increased? (Assume that the standard deviation has not changed.) Perform a one-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places, and round your responses as specified in the table. The null hypothesis: H0: The alternative hypothesis: H1: The type of test statistic: (Choose one)ZtChi squareF The value of the test statistic:(Round to at least three decimal places.)…
The article “Occurrence and Distribution of Ammoniumin Iowa Groundwater” (K. Schilling, WaterEnvironment Research, 2002:177–186) describesmeasurements of ammonium concentrations (inmg/L) at a large number of wells in the state of Iowa.These included 349 alluvial wells and 143 quaternarywells. The concentrations at the alluvial wells averaged0.27 with a standard deviation of 0.40, and thoseat the quaternary wells averaged 1.62 with a standarddeviation of 1.70. Find a 95% confidence interval forthe difference in mean concentrations between alluvialand quaternary wells.

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