4. Suppose that we want to compare the cholestrol contents of four competing diet foodson the basis of the following data (in milligrams per package) which were obtained forthree 6-ounce packages of each of the diet foods:Diet food A: 3.6 4.1 4.0 Diet food B: 3.1 3.2 3.9 Diet food C: 3.2 3.5 3.5 Diet food D:3.5 3.8 3.8a) Fill in the blanks below.b) Test at the 0.05 level of significance whether the differences among meansobtained for the four competing diet foods (Diet A, B, C, D) are significant?Etable=4.07)ONE-WAY ANOVA TABLESource ofDegrees ofSum of SquaresMean SquareFVariationFreedomTreatments?0.54??Error???Total?1.18

The main objective of an ANOVA (one-way) is to compare the means of more than two means to identify…

Answered: 4. Suppose that we want to compare the…

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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Thomas wants to compare the mean concentration of carbon monoxide (CO) on residential versus commercial streets, since these differ in terms of car traffic. In each of three neighborhoods of Montréal (named A, B, and C below), he randomly chooses four locations for each type of street, for a total of 24 observations (2 street types x 3 neighborhoods x 4 locations). At each location, he measures CO concentration in the air over a period of 10 hours (8:00 AM-6:00 PM), and obtains the following data (in ppm/h). Question: Test whether or not the difference between residential and commercial streets in mean atmospheric CO concentration is the same among the three neighborhoods, and whether or not CO concentration in the air is the same, on average, for the two types of streets. Note that Neighborhood is considered a random block factor in the ANOVA. Use significant level= 0.05.
Perform PCA or principle component analysis on the following data: х1 x2 x3 810.6 13.4 42.93 1775 24.2 32.319 430.4 5.7 60.434 459.8 9 21.398 802.4 13.9 55.778 279.6 20.4 53.236 288.4 4.6 63.208 152.7 7.3 59.727 253.4 9.9 48.037 358.6 13.5 48.288 72 12.8 36.507 205 5.9 37.195 253.6 15.8 36.964 416.5 12.3 42.83 1075.9 17.1 39.684 Answer the following questions based on the PCA: • How many principle components were created? • What percent of total variance is accounted for by the calculated principal components? (Round to 2 decimal places) • What are the weights for computing the first principle component scores? (Round to 4 decimal places) o x1: • x2: o x3:
Scientists have discovered a new bird species; however, they only found 15 birds of such species. They measured the height (in cm) of these 10 birds:12.94, 5.80, 15.47, 14.14, 7.48, 9.21, 9.79, 8.86, 17.75, 10.39. I entered the data into R as shown below: bird <- c(12.94, 5.80, 15.47, 14.14, 7.48, 9.21, 9.79, 8.86, 17.75, 10.39) Treat this data as population data. Which of the following R code computes the variance of the height of the birds? A. var(bird) B. sum((bird - mean(bird))^2)/length(bird) C. mean((bird - mean(bird))^2) D. sum((bird - mean(bird))^2)/9 E. B and C F. A and D G. B and D H. A and C
rofessor Cornish studied rainfall cycles and sunspot cycles. (Reference: Australian Journal of Physics, Vol. 7, pp. 334-346.) Part of the data include amount of rain (in mm) for 6-day intervals. The following data give rain amounts for consecutive 6-day intervals at Adelaide, South Australia. 7 28 7 1 69 3 1 4 22 7 16 4 54 160 60 73 27 3 3 1 7 144 107 4 91 44 1 8 4 22 4 59 116 52 4 155 42 24 11 43 3 24 19 74 26 63 110 39 34 71 52 39 8 0 15 2 14 9 1 2 4 9 6 10 (i) Find the median. (Use 1 decimal place.)(ii) Convert this sequence of numbers to a sequence of symbols A and B, where A indicates a value above the median and B a value below the median. Test the sequence for randomness about the median at the 5% level of significance. (b) Find the number of runs R, n1, and n2. Let n1 = number of values above the median and n2 = number of values below the median. R n1 n2 (c) In the case, n1 > 20, we cannot use Table 10 of Appendix II to find the critical…
Consider the following data on x = weight (pounds) and y = price ($) for 10 road-racing bikes. Brand Weight Price ($) A 17.8 2,100 В 16.1 6,350 C 14.9 8,370 15.9 6,200 E 17.2 4,000 13.1 8,500 G 16.2 6,000 17.1 2,480 I 17.6 3,300 14.1 8,000 These data provided the estimated regression equation ŷ = 28,532 – 1,438x. For these data, SSE = 7,779,221.53 and SST = 52,710,800. Use the F test to determine whether the weight for a bike and the price are related at the 0.05 level of significance. %3D State the null and alternative hypotheses. Ho: Bo + 0 Ha: Bo = 0 O Ho: Bo = 0 Ha: Bo + 0 O Hoi Bq = 0 H: B1 + 0 O Ho: Bq z 0 Ha: B1 < 0 O Ho: Bq # 0 Ha: B1 = 0
To test whether the mean time needed to mix a batch of material is the same for machines produced by three manufacturers, the Jacobs Chemical Company obtained the following data on the time (in minutes) needed to mix the material. Manufacturer 1 2 3 25 34 15 31 32 14 29 37 18 27 33 17 a. Use these data to test whether the population mean times for mixing a batch of material differ for the three manufacturers. Use a = 0.05. Sum of squares, treatment = Sum of squares, error = Mean squares, treatment = mean squares, error = Calculate the value of the test statistic (to 2 decimals). The P-value is: Less than 0.01, between 0.01 and 0.025, between 0.025 and 0.05, between 0.05 and 0.10, greater than 0.10 What is your conclusion? b. At the a = 0.05 level of significance, use Fisher's LSD procedure to test for the equality of the means for manufacturers 1 and 3. What conclusion can you draw after carrying out this test?
The following data was reported on total Fe for four types of iron formation (1 carbonate, 2 silicate, 3 magnetite, 4 hematite). 1: 21.0 28.1 27.8 27.0 27,8 25.2 25.3 27.1 20.5 31.5 2: 26.2 24.0 26.2 20.2 23.6 34.0 17.1 26.8 23.7 25.0 3: 29.6 34.0 27.5 29.4 26.4 26.2 29.9 29.5 30.0 35.5 4: 37.1 44,2 34.1 30.3 31.8 33.134.1 32.9 36,3 25.3 A USE SALT Carry out an analysis of variance F test at significance level 0.01. State the appropriate hypotheses. H at least two 's are equal Ho Hi= Ha = H4 H at least two 's are unequal O Ho = = 4 H al four s are unequal H all four 's are equal
The US Department of Agriculture collected nutrient data on various types of cheeses. Two nutrients of concern to people trying to eat healthier are saturated fat and sodium. The given JMP applet shows scatterplots of the amount of sodium in milligrams by the amount of saturated fat in grams for these cheeses.t O JMP Applet jmp ? Sodium (mg) By Saturated Fat (g) Sodium (mg) By Saturated Fat (15 g - 21 g) 2000 2000 1500- 1500 1000- 1000- 500- 500- 0- 0- 20 15 16 20 21 Saturated Fat (g) Saturated Fat (g) Sodium (1,000 mg - 2,000 mg) By Saturated Fat (g) 1800- 1000- 1400- 1200- 1000- 10 15 20 Saturated Fat (g) II (Bu) unipos III (Bu) unipos (Bu) unipos
The alcohol content of wine depends on the grape variety, the way in which the wine is produced from the grapes, the weather, and other influences. Here are data on the percent of alcohol in wine produced from the same grape variety in the same year by 16 winemakers in the same region of Italy: 12.86 12.88 12.81 12.70 12.51 12.60 12.25 12.53 13.49 12.84 12.93 13.36 13.52 13.62 12.25 13.16 Give a 95% confidence interval for the mean alcohol content of wine of this type.
The following figures show the number of passengers carried on each of 50 journeys by an aircraft with a seating capacity of 100. Calculate: (i) the average capacity used and (ii) if 65 passengers is the smallest profitable load the proportion of flights which were unprofitable. 10 18 61 63 72 71 82 25 45 66 68 95 92 31 41 56 33 78 65 72 74 89 67 68 32 46 49 35 37 43 55 57 69 72 84 69 92 75 83 68 75 42 45 39 11 37 38 62 89 72
Several methods of estimating the number of seeds in soil samples have been developed by ecologists. An article gave the accompanying data on the number of seeds detected by the direct method and by the stratified method for 27 soil specimens. Specimen Direct Stratified 1 21 6 2 32 38 3 0 6 4 60 58 5 20 52 6 61 61 7 40 26 8 6 6 9 12 6 10 92 100 11 1 0 12 66 58 13 78 66 14 21 52 Specimen Direct Stratified 15 32 26 16 0 0 17 38 38 18 18 12 19 92 92 20 1 12 21 40 46 22 21 21 23 0 0 24 6 12 25 12 40 26 18 12 27 40 78 Do the data provide sufficient evidence to conclude that the mean number of seeds detected differs for the two methods? Test the relevant hypotheses using ? = 0.05. (Use ?direct − ?stratified.) Find the test statistic. (Round your answer to two decimal places.) t = Find the df. (Round your answer down to the nearest whole number.) df = Use technology to find the P-value. (Round your answer to four…
The densities of several common metals are shown in the following table. Metal Density (g/cm³) iron 7.87 silver 10.49 lead 11.36 zinc 7.13 aluminum 2.70 For her chemistry lab, Kamila needs to identify three metal samples by density. The data she collected is shown in the following table. The metal samples are all rectangular prisms.

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