The thickness of a plastic film (in mils) on a sub-strate material is thought to be influenced by the temperatureat which the coating is applied. A completely randomizedexperiment is carried out. Eleven substrates are coated at125°F, resulting in a sample mean coating thickness of= 103.5 and a sample standard deviation of s1 = 10.2.Another 13 substrates are coated at 150°F, for which , = 99.7and s2 = 20.1 are observed. It was originally suspected thatraising the process temperature would reduce mean coatingthickness.Find a 99% confidence interval on the difference in meancoating thickness Hi - H2.Assume each population is normally distributed but that theirvariances are not equal.What is the lower bound? Two decimal places

The random variable is coating thickness. There are two independent samples which are 125F and 150F.…

Answered: The thickness of a plastic film (in…

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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Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants , insulating materials , and lubricants in electrical equipment. Disposal of the items containing less than 50 parts per million ( ppm) PCM is generally not regulated . A certain kind of small capacitor contains PCB with a mean of 48.2 ppm and a standard deviation of 8 ppm. The Environmental Protection Agency takes a random sample of 37 of these small capacitors , planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 49 ppm or more . Find the probability that the disposal of such capacitors will be regulated. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places .
A lumber company is making boards that are 2599.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 23 is made, and it is found that they have a mean of 2600.3 millimeters with a standard deviation of 13.0 A level of significance of 0.05 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
A major car ürer wants tô tést á ñew engine to determine whether it meets air pollution standards. The mean emission of all engines of this type must be less than 20 ppm of carbon. 10 engines are setup for testing and produce an average emission of 17.57 ppm with a sample standard deviation of 2.95. Can the manufacturer be certain within a level of significance of 0.01 that his engine's average emissions are less than 20 ppm. Use a = 0.01, a. Setup the null and alternate hypothesis b. Choose an appropriate test statistic, fill in the all of the information, and solve for the test statistic. C. Would you reject or not reject Ho, demonstrate why you made your choice. d. Based on your analysis above, can the manufacturer be certain his engines meet the specification? Make an appropriate statement.
The daily sleep duration among college students is normally distributed with a mean of 8.13 and standard deviation of 1.87. You want to use a sample size such that 95% of the averages fall within ±15±15 minutes (.25 of an hour) of the true mean of 8.13. Determine the smallest number of students you need to sample.
Do students who are members of fraternities or sororities have GPAs different from the student body as a whole? A random sample of 123 "greeks" has been selected from the student body of a large university. The GPA for the student body as a whole is 2.59 and the mean for the sample of "greeks" is 2.47 with a standard deviation of .34. Is the difference statistically significant at the alpha=.05 level? Show the results of your t-test and state whether that means the difference is significance or not.
Bone mineral density (BMD) is a measure of bone strength. Studies show that BMD declines after age 45. The impact of exercise may increase BMD. A random sample of 59 women between the ages of 41 and 45 with no major health problems were studied. The women were classified into one of two groups based upon their level of exercise activity: walking women and sedentary women. The 39 women who walked regularly had a mean BMD of 5.96 with a standard deviation of 1.22. The 20 women who are sedentary had a mean BMD of 4.41 with a standard deviation of 1.02. Which of the following inference procedures could be used to estimate the difference in the mean BMD for these two types of women
A researcher selected a sample of 156 former student leaders from a list of graduates of a large university. She discovered that it had taken an average of 4.97 years for the graduates to finish their degrees, with a standard deviation of 1.23. The average for the entire student body is 4.56 years. Is the difference statistically significant? Alpha = 0.05; two-tailed test.
Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than 50 parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of 47.7 ppm and a standard deviation of 5 ppm. The Environmental Protection Agency takes a random sample of 38 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 49.5 ppm or more. Find the probability that the disposal of such capacitors will be regulated. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
In a study of microplastics in our environment, it was determined that there are 5.25 trillion plastic pieces floating in the ocean, weighing more than 250,000 tons. In a recent expedition to examine whether increases in plastic production have led to changes in ocean microplastics, 16 samples were taken at various locations in the Pacific Ocean. It was determined that the average concentration was 9.5 particles per liter of ocean water with a sample standard deviation of 6. In one of the earliest research expeditions to study microplastics in the ocean conducted in 2009, it was determined that the average concentration of microplastics was 6 particles per liter (consider this the population or reference mean). What is the critical value for the two-tailed alternative hypothesis at alpha = 5%? (Hint: This is the value in the table that you will compare your test statistic to in order to determine the outcome of the hypothesis test). 2.131 1.746 2.120 1.753
Polychlorinated biphenyl (PCB) is among a group of organic pollutants found in a variety of products, such as coolants, insulating materials, and lubricants in electrical equipment. Disposal of items containing less than 50 parts per million (ppm) PCB is generally not regulated. A certain kind of small capacitor contains PCB with a mean of 48.2 ppm and a standard deviation of 5 ppm. The Environmental Protection Agency takes a random sample of 37 of these small capacitors, planning to regulate the disposal of such capacitors if the sample mean amount of PCB is 49.5 ppm or more. Find the probability that the disposal of such capacitors will be regulated. Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.
A recent television news station reports that the average Body Mass Index (BMI) (a measure of a person’s body composition) for males is 10kg/m2. A local university believes that this is unusually low and suspects that males are actually higher than their claim. They conduct a study with 20 undergraduate males randomly selected from their campus. A sample mean of 16.5kg/m2 with a standard deviation of 3.2kg/m2 was obtained. Using an alpha of.05 is there enough evidence to warrant rejection of the news station’s claim of 10kg/m2?? a. Write your hypotheses for this scenario. b. Is this a one tailed or two tailed test? i. Why? c. What statistical test would be used for this scenario? i. Explain why.
A randomized controlled trial is run to evaluate the effectiveness of a new drug for asthma in children. A total of 250 children are randomized to either the new drug or a placebo (125 per group). The mean age of children assigned to the new drug is 12.4 with a standard deviation of 3.6 years. The mean age of children assigned to the placebo is 13.0 with a standard deviation of 4.0 years. Suppose that there are 63 boys assigned to the new drug group and 58 boys assigned to the placebo group. Is there a statistically significant difference in the proportions of boys assigned to the treatments? Run the appropriate test at a 5% level of significance.

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