b) A paint company has developed a new paint formula which should have a faster drying timecompared to the old formula. Paint drying time is known to be normally distributed, andfrom previous tests it is known that the original paint formula has a mean drying time ofM₁ = 45 min. The company's R&D scientists believe the new formula will have a mean dryingtime of μ₂ = 35 min (that is, they expect the new formula to dry an average of 10 min fasterthan the old formula, or that μ₁ −μ₂ = 10). They are early in the development process andare not sure what the population variances are.A scientist takes 15 samples of each paint formula and determines the mean drying time foreach batch to be X₁ = 43 min and X₂ = 36 min with sample standard deviations equal toS₁ = 5.4 and s₂ = 3.7, respectively. Find a 99% confidence interval on the difference inaverage lifetime between the two populations (μ₁-M₂).<μ<

Obtain the 99% confidence interval on the difference in average lifetime between the two…

Answered: A paint company has developed a new…

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 companies from the Forbes 500 list was selected, and the relationship between sales, in hundreds of thousands of dollars, and profits, in hundreds of thousands of dollars, was investigated by regression. The simple linear regression model displayed was used: profits = a + B (sales), where the deviations were assumed to be independent and Normally distributed, with mean 0 and standard deviation o. This model was fit to the data using the method of least squares. The results displayed were obtained from statistical software. 2 = 0.662 S = 466.2 Parameter Std. err. of Parameter estimate parameter est. -176.644 61.16 0.092498 0.0075 Suppose the researchers test the hypotheses Ho: P = 0, II, : A > 0. The P-value of the test is: less than 0.01. between 0.05 and 0.01. O between 0.10 and 0.05. greater than 0.10. hp
N= 150 observations were collected on a time series that was identified as a AR(2) time series. The following statistics were computed from the data. Mean - 45.0 Variance 15.6 Autocorrelation function (up to lag 5) r1 = 0.80, r2 = .50, rз = .26, r4 = -.10, rs = 0.08: == Estimate the parameters of the model using the method of moments.
Suppose you are to estimate a simple regression for the following population model: Y=B₁ + B₁X + µl From a population of over thousands of observations, a small number of samples were randomly selected. The following is some of the information from the randomly selected sample.
Before surgical removal of a diseased parathyroid gland, two tests are often performed: the standard intact test and the turbo test. Both tests measure parathyroid hormone (PTH, in ng/l), but the turbo test is very expensive. Researchers obtained data from both tests in a sample of 48 patients to predict turbo test results (y) from standard intact test results (x). The data ranged from roughly O to 500 ng/l, and a scatterplot showed a clear linear relationship. The published findings given are summarized exactly: y = 1.08x-4.36(r = 0.97; n = 48) Roughly what percent of the variation in turbo test results can be explained by this regression model? It is not possible to answer with the information provided. 94% 98.5% 97%
Show step by step 1 Simulate the failure times of 100 units randomly selected from a Weibull distributionwith characteristic life θ = 100 and shape parameter α = 3. Plot the histogram ofthese 100 data points and comment on this histogram. 2. Suppose the data of the last question came from a life testing but the test was stoppedat the 50-th failure. Re-organize the data set and re-plot the histogram. Compare thisplot with the previous plot and comment on these plots. Show step by step
imagine a large class where nearly everyone scores between 83.84%, with hardly any dispersion beyond this narrow range (so it would appear to have a very narrow peak). How would your describe this distribution of data in terms of kurtosis?
The US government is interested in understanding what predicts death rates. They have a set of data that includes the number of deaths in each state, the number of deaths resulting from vehicle accidents (VEHICLE), the number of people dying from diabetes (DIABETES), the number of deaths related to the flu (FLU) and the number of homicide deaths (HOMICIDE). Your run a regression to predict deaths and get the following output: At α = .10, which variable(s) is/are significant predictors of deaths?
4. A simple linear regression is fit to a dataset. Unfortunately, the corresponding ANOVA table is not complete because some quantities in the table are missing due to unknown digital errors. Calculate the missing values, denoted by "?", in the ANOVA table based on the other available values. Is this regression model significant (α = 0.05)? Source Regression Residual Total df ? ? 21 SS ? ? ? MS = SS/df ? 1.13 F-Ratio 430.65 p-value ?
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Students who complete their exams early certainly can intimidate the other students, but do the early finishers perform significantly differently than the other students? A random sample of 37 students was chosen before the most recent exam in Prof. J class, and for each student, both the score on the exam and the time it took the student to complete the exam were recorded. a. Find the least-squares regression equation relating time to complete (explanatory variable, denoted by x, in minutes) and exam score (response variable, denoted by y) by considering Sx = 15, sy = 17,r = 39.706, x = 90, ỹ = 78 b. The standard error of the slope of this least-squares regression line was approximately (Sp) is 20.13. Test for a significant positive linear relationship between the two variables exam score and exam completion time for students in Prof. J's class by doing a hypothesis test regarding the population slope B1. Write the null and Alternate hypothesis and conclude the results. (Assume that…
Suppose you run a regression y=alpha + beta*x + u. You know that the model sum of squares equal 2998.9, residual sum of squares equals 571,612.8, and residual mean squares (MS) squals 412.41. What is the number of observations in your sample?

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