Applying the Central Limit Theorem: The amount of contaminants that are allowed in food products isdetermined by the FDA (Food and Drug Administration). Common contaminants in cow milk includefeces, blood, hormones, and antibiotics. The current amount of somatic cells (common name "pus")allowed in 1 cc of cow milk is currently set at 750,000. Suppose a random sample of 55 1 ccspecimens is gathered and results in a sample mean of 783377 pus cells.a. Why is the samplingdistribution approximately normal?b. Assuming a population mean of 750,000 cells and a populationstandard deviation of 146000 cells: What is the mean of the sampling distribution?c. What is thestandard deviation of the sampling distribution?d. What is the probability that a simple randomsample of 55 1 cc specimens has a mean of at least 783377 pus cells?

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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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1. Tim Hortons wanted to estimate the difference in the mean amounts of caffeine in two brands of coffee. They took a sample of 18-lbs jars of Brand I and another sample of 13-lbs jars of Brand II coffee. The following summary data (sample statistics) are collected? nį = 10 x, = 23 S1 = 3 Brand I Brand II n2 = 12 x2 = 25 S2 = 4 Assume that the two populations are normally distributed. A. Test at 5 % level of significance, whether there is a difference in the mean amounts of caffeine between the 2 brands of coffee. B. Construct a 95% Confidence Interval to estimate the difference in the mean amounts of caffeine in 2 brands of coffee. C. Does the result in part b) confirm your findings from part a)?
A state fisheries commission wants to estimate the number of bass caught in a given lake during a season in order to restock the lake with the appropriate number of young fish. The commission could get a fairly accurate assessment of the seasonal catch by extensive “netting sweeps" of the lake before and after a season, but this technique is much too expensive to be done routinely. Therefore, the commission samples a number of lakes and record the seasonal catch (thousands of bass per square mile of lake area) and size of lake (square miles). A simple linear regression was performed and the following R output obtained. Estimate Std. Error t value Pr(>|t|) (Intercept) 2.5463 0.4427 5.7513 0.0000 size 0.0667 0.3672 0.1818 0.8578 If a scatterplot showed a non-linear relationship between the response and explanatory variables, what should be done? O Nothing. Continue the analysis as is. Stop the analysis. Perform a natural log transformation on the response variable first. O Perform a…
If a point on a control chart falls outside one of the control limits, this suggests that the process variation is random and should not be investigated. O a. TRUE O b. FALSE PAGE NEXT PAGE ype here to search 99+ SUS
Suppose that you plot the residuals for your sample and get Figure 2. You should conclude that Select one: a. possibly homoskedastic and you would perform a correction for homoskedasticity. b. likely homoskedastic. c. possibly heteroskedastic and you would perform a formal test for heteroskedasticity. d. definitely heteroskedastic.
9. Auto Exhaust and Lead Exposure Researchers interested in lead exposure due to car exhaust sampled the blood of 19 police officers subjected to constant inhalation of automobile exhaust fumes while working traffic enforcement in a primarily urban environment. The blood samples of these officers had an average lead concentration of 11.2µg/dl and a SD of 4.5µg/dl; a previous study of individuals from a nearby suburb, with no history of exposure, found an average blood level concentration of 7.2μg/dl. (a) Test the hypothesis that the downtown police officers have a higher lead exposure than the officers in the previous study. Be sure to interpret your results in context. a = = 0.05 (b) Explicitly state and check all conditions necessary for inference on this data. (c) Based on your preceding result, without performing a calculation, would a 90% confidence interval for this difference contain 0? Explain why or why not.
Match the definition in column X with the correct term in column Y.
2. A school has 6,000 students with a mean weight of 80lbs, with a standard deviation of 25 lbs. If you draw a random sample of 50 students, what is the mean µz , variance o?z , and standard deviation oz of the sampling distribution of the sample mean? (Show solution to gain point in each correct answer Hx = o?x = Oz =
34) If a population exhibits a skew of -5.00 and an excess kurtosis of 5.00 which of the following is true? The population mean exceeds the median. The population variance exceeds the standard deviation. The population standard deviation exceeds the variance. The population median equals the mean. The population median exceeds the mean.
5. A quality control engineer found that the inner and outer diameters of their ball bearings, denoted respectively as X and Y, are random variables with E(X|Y = y) = 0.7 – 0.3y inches and Var(X|Y = y) = 0.0004y for all values of y. From his past experience he also knew that the mean and variance of the outer diameters were E(Y) = 0.7 inches, and Var(Y) squared inches. = 0.0001 %3D • (i) What are the conditional random variables, E(X|Y) and Var(X|Y)? • (ii) Find the mean of the inner diameters, E(X). • (ii) Find the variance of the inner diameters, Var(X).
You intend to conduct a test of homogeneity for a contingency table with 5 categories in the column variable and 4 categories in the row variable. You collect data from 553 subjects.What are the degrees of freedom for the χ2 distribution for this test? d.f. =
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Suppose a certain retailer sells several models of refrigerators. A random sample of the models sold by this retailer and their corresponding cubic feet (cu. ft.) and list price can be found below. Model Model 1 Model 2 Model 31 with Thru-the-Door Ice and Water. Model 4 Model 5 Model 6 with Thru-the-Door Ice and Water Model 7 Model 8. Model 9 with Thru-the-Door Ice and Water Model 10 with Thru-the-Door Ice and Water Model 11 with Thru-the-Door Ice and Water Model 12. Model 13 with Thru-the-Door Ice and Water Model 14 Model 14 Model 15 Model 16 with Thru-the-Door Ice and Water Model 17 Model 18 with Thru-the-Door Ice and Water Model 19 with Thru-the-Door Ice and Water Model 20 with Thru-the-Door Ice and Water Model 21 Cu.Ft. List Price 18.3 Ho: B₂ 20 H₂: B₁ 0 ⒸH₁: B₁ = 0 H₂: P₁0 24.8 25.4 19.3 17.3 19.6 25.0 25.4 26.0 25.6 18.0 25.0 20.2 24.5 $1,299.99 20.2 15.5 28.2 27.8 $899.99 23.6 $1,799.99 $1,799.99 $749.99 $599.99 $1,619.99 $999.99 $1,299.99 $1,299.99 $1,099.99 $679.99 $2,199.99…

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