5. A random sample of 12 shearing pins is taken in a study of theRockwell hardness of the head of the pin. Measurements on theRockwell hardness were made for each of the 12, yielding an averagevalue of 48.50 with a sample variance of 2.25. Assuming themeasurements to be normally distributed, construct a 90% confidenceinterval for the mean Rockwell hardness.6. A machine is being used for packaging popcom. It is known that thestandard deviation of the net weight of all popcom is 0.78g. A qualityengineer selects a sample of 12 consecutive popcorm packages filledduring the production process and gets a mean net weight of 15.4g.Construct a 98.2% confidence interval for the true net weight for alsuch popcom packages.7. A researcher wants to estimate the average weight of all mice afterthey were given some nutritious herb extract. From experience it isknown that the standard deviation of all mice is 123g. A random„sample of 10 mice is taken and the data (in grams) below is obtained:39.843.345.142.344.541.440.640.243.945.3(a) Find a point estimate for the true mean weight of all such mice.(b) Construct a 96.5% confidence interval for the true imean weight ofall such mice.8. A study on hearing impairment among workers in a construction sitebas been done. A random sample of 33 workers has been tested andthe results are as follows:

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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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A random sample of 19 shearing pins is taken in a study of the RockwelI hardness of the pin head. Measurements on the Rockwell hardness are made for each of the 19, yielding an average value of 47.50 with a sample standard deviation of 1.8. Assuming the measurements to be normally distributed, construct a 95% confidence interval for the mean Rockwell hardness.
Sheldon is the manager for Kara Tyres. He suspects that the claim that their tyres can go the minimum of 13800 km without being worn out is incorrect. He is going to address this issue in his annual report. He has sampled a group of 25 tyres, and calculated that the average kilometers that his sample of tyres can go before being worn out is 13690, with the sample standard deviation of 110 km. What should Sheldon write in his annual report at 0.01 significance level?
A random sample of 100 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each household .The average usage was found to be 10.5 kWh. In a very large study in the previous year it was found that the standard deviation of the usage was 3.2 kWh. Assuming the standard deviation is unchanged and that the usage is normally distributed, calculate a 90% confidence interval for the mean usage (round to two decimals) a. (9.68 , 11.30) O b. (9.87 , 11.10) O c. (7.05 , 7.95) O d. None of these e. (9.97 , 11.00)
An avionics company uses a new production method to manufacture aircraft altimeters. A single random sample of new altimeters resulted in the errors listed below. Use a 5% significance level to test the claim that the new production method has errors with a standard deviation greater than 32.2 ft, which was the standard deviation for the old production model (o). If it appears that the standard deviation is greater, does the new production method appear to be better or worse than the old method? Should the company take any action? -42 78 -22 -72 -45 15 17 51 -5 -53 -9 -109 Find the upper and lower boundaries of the 95% confidence interval for o. 98 37 32 73 89
Listed in the data table are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.05 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents. City_#1 City_#2108 11786 53121 100116 85101 83104 107213 110113 111290 142100 133266 101145 209 What are the null and alternative hypotheses? Assume that population 1 consists of amounts from city #1 levels and population 2 consists of amounts from city #2? The test statistic is? The P-value is? State the conclusion for the test?
An engineer working for a tire manufacturer investigates the average life of a new material to be used in the manufacturing process. For this purpose, he builds a sample of 13 tires and tests them in a laboratory until the end of their useful life is reached. The data obtained from the sample are as follows: average of 60897.9 km and standard deviation of 2734.8 km. The engineer would like to demonstrate that the average service life of the tire with the new material exceeds 60,000 km. a) State the null and alternative hypothesis to be stated in this experiment. Test the stated hypotheses using an α = 0.05 What conclusions are reached? b) Find a 95% confidence interval for the average tire life with the new material. Interpret your answer. (RESPOND MANUALLY) (RESPOND MANUALLY)
Listed in the data table are amounts of strontium-90 (in millibrcquerels or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from residents in two cities. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Use a 0.10 significance level to test the claim that the mean amount of strontium-90 from city #1 residents is greater than the mean amount from city #2 residents. Find the test statistic, p value, and confidence interval
A random sample of 11 shearing pins is taken in a study of the Rockwell hardness of the pin head. Measurements on the Rockwell hardness are made for each of the 11, yielding an average value of 48.50 with a sample standard deviation of 1.6. Assuming the measurements to be normally distributed, construct a 95% confidence interval for the mean Rockwell hardness.
An SRS of 20 orangutans is selected, and 65 cc of blood is to be drawn from each orangutan using a 100 cc syringe. In the sample, the mean volume is 64 cc and the standard deviation is 12 cc. Assume that in the population of all such procedures, the amount of blood drawn follows ą Normal distribution with mean u. A 90% confidence interval for the population mean volume based on these data is
One method for measuring air pollution is to measure the concentration of carbon monoxide, or CO, in the air. Suppose Nina, an environmental scientist, wishes to estimate the CO concentration in Zagreb, Croatia. She randomly selects 45 locations throughout the city measures the CO concentration at each location. Based on her 45 samples, she computes the margin of error for a 95% t-confidence interval for the mean concentration of CO in Zagreb, in µg/m³, to be 4.28. What would happen to the margin of error if Nina decreases the confidence level to 90%? Nina increases the confidence level to 99%? Nina decreases the sample size to 33 locations? Nina increases the sample size to 65 locations? Answer Bank Increase Stay the same Decrease
In the manufacture of steel rollers to fit an assembly, the external diameter is considered to be a random variable with mean equal to 23 mm and variance equal to 0.0036 cm2. 1.5 is supported standard deviations more than the mean and 3.5 standard deviations below average. A piece with a diameter below such specifications is considered waste, whereas a piece with a diameter larger than specified must be reprocessed. Which is the percentage of pieces that:to. They are being wasted.b. They need to be reprocessed.c. Acceptable.d. If you want to establish that the reprocessing is 5% of the rollers and waste of 1%, than specification limit would recommend.

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