Mod3 Discussion Post

Exercise 4.4: Seven students measured the length of a rod to be as shown below: Student No. 1 4 6. 7 Length (cm) 87.5 87.3 87.4 87.6 87.8 87.2 87.1 (a) What is the best estimate for the length of the rod? (b) What is the sample standard deviation in the length of the rod? (c) What will be the uncertainty in the length of the rod?

An engineer measures the diameter of 20 tubes selected at random from a large shipment. The sample mean is 48.5 mm and S- 9.4 mm. The manufacturer of the tubes claims that 2 = 42.1 mm. Is this claim supported by data set? for 90% probability? where a' is the true or the estimate value O No O yes

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Areas Under the Standard Normal Curve-The Values Were Generated Using the Standard Normal Distribution Function of Excel Note that the standard normal curve is symmetrical about the mean. z 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 1 0.95 0.96 0.97 0.98 0.99 1.01 1.02 1.03 1.04 1.05 Mean - 0 1.06 1.07 1.08 1.09 A 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359 0.0398 0.0438 0.0478 A 0.3186 0.3212 0.3238 0.3264 0.3289 0.3315 0.3340 0.3365 0.3389 Z 0.3413 0.3438 0.3461 0.3485 0.3508 0.3531 0.3554 0.3577 0.3599 0.3621 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 1.12 1.13 1.14 1.15 1.16 1.17 A z 0.0517 0.0557 0.26 0.27 0.28 0.29 0.0596 0.0636 0.0675 0.3 0.0714 0.31 0.0753 0.32 0.0793 0.33 0.0832 0.34 0.0871 0.35 0.0910 0.0948 0.0987 1.18 1.19 1.2 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 A 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.36 0.3830 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.37…

As an engineer working for a water bottling company, you collect the following data in order to test the performance of the bottling systems. Assume normal distribution. Milliliters of Water in the Bottle Frequency 485 490 milliliters 495 500 505 510 515 What is the mean (in milliliters)? milliliters What is the standard deviation (in milliliters)? What is the z value corresponding to 490 milliliters? Z = 6 12 20 33 18 11 00 8

A temperature measurement system has the following specifications: -128 to 781°C Range Linearity error 0.29% FSO Hysteresis error 0.12% FSO Sensitivity error 0.04% FSO Zero drift 0.32% FSO FSO stands for "Full Scale Output". Estimate the overall instrument uncertainty for this system based on the available information. Use the maximum possible output range over the FSO in your computations.

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The life in hours of a 60-watt light bulb is known to be normally distributed with o=10 hours. A random sample of 16 bulbs has average life of =3000 hours. (a) Construct a 95% two-sided confidence interval on the mean life of the light bulb. (b) Construct a 95% lower-confidence bound on the mean life of the light bulb.

2. An electrical firm manufactures light bulbs that have a lifetime that is approximately normally distributed with a standard deviation of 36 hours. A lifetime test of n=36 samples resulted in the sample average of 1510 hours. Assume the significance level of 0.05. (a) Test the hypothesis Ho: µ = 1000 versus H1: µ# 1000 using a p-value. (b) Test the hypothesis using critical region(s) approach. (c) Suppose that the true mean lifetime is 1510 hours. What is type Il error probability for this| two-sided test.

A random sample of 20 students yielded a mean of = 72 and a variance of s2 = 16 for scores on a college placement test in mathematics. Assuming the scores to be normally distributed, construct a 98% confidence interval for σ2.

A small sample (N = 7) of the static coefficient of friction (µ) between two materials is measured with the following data set: 0.0043 0.0050 0.0053 0.0047 0.0031 0.0051 0.0049 Test the data for outliers. Determine the mean value and its confidence.

compute the 95 confidence intervals for the inventory of a series of 12 replication of the simulation of a system, where the VERAGE INVENtory is 1000 units and sample standard deviation is 38

A random sample of 64 items is selected from a population of 400 items. The sample mean is 200. The population standard deviation is 48. From these data, the 95% confidence interval to estimate the population mean would be 189.21 to 210.79 B. 193.45 to 211.09 188.24 to 211.76 D. 190.13 to 209.87

Calculate the absolute uncertainty, fractional uncertainty, and percentile uncertainty

4. In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 450 of 1000 urban residents favor the construction while only 240 of 800 suburban residents are in favor. (a) Is there a significant difference between the proportion of urban and suburban residents who favor construction of the nuclear power plant? Test with p-value at a = 0.05. (b) Construct a 95% confidence interval for the difference of favor proportions between urban residents and suburban residents and test if there is a significant difference between the proportion of urban and suburban residents who favor construction of the nuclear power plant. (You need to explain how you make the conclusion). (c) By using critical region(s) test if there is a significant difference between the proportion of urban and suburban residents who favor construction of the nuclear power plant. |

An electrical firm manufactures light bulbs that have a lifetime that is approximately normally distributed with a standard deviation of 36 hours. A lifetime test of n=36 samples resulted in the sample average of 1510 hours. Assume the significance level of 0.05. (a) Test the hypothesis HO:µ=1500 versus H1:µ#1500using ap-value. (10pts) (b) Calculate the power of the test if the true mean lifetime is 1510. (10pts)

Statistical Inference