ANOVA Practice Problems 1. Suppose that a random sample of n = 5 was selected from the vineyard properties for sale in Sonoma County, California, in e...
A certain electromagnetic wave has a wavelength of 625 nm. a.) What is the ... ( Note: All electromagnetic travels at the speed of light in a vacuum). 2.8 x 107 mi x 1 ... λ = c = 2.998 x 108 m x 1 nm = 4.0 x 102 nm ν 7.5 x 1014 s-1. 10-9 m b.) Calcu
One Way ANOVA - II Orthogonal Contrasts ANOVA Models Random vs Fixed EffectsRandom vs. Fixed Effects Testing Assumptions Normality Homoscedasticity
Slower car . t. . . . 0 t1t2 t3 t4 t01t2t3t4. Time. "Practice Problems . 3.2 Motion with Constant Acceleration pages 65—71 page 65. 18. A golf ball rolls up a hill toward a ... 5.1 s ' car slows from 22 m/s to 3.0 m/s at a constant rate of 2.1 m/s2.
Comparative Advantage Practice Problems . Absolute Advantage: makes the most of a good (if using similar resources) Comparative Outputs: lowest opportunity costs of
Waves Practice Problems. PSI AP Physics B. Name___________________________________. 1. In a wave, the distance traveled by a wave during one period is called: (A) Amplitude (B) Frequency (C) Wavelength (D) Displacement. 2. A stretched wire resonates
Please do #18 in chapter 12 of your text. a. This increases the [H 2], which will increase the rate, but has no effect on k ... KINETICS Practice Problems and Solutions
Determining Comparative Advantage: Input method In order to produce 1 ton of output, Mexico and the USA require the following amount of land (in acres)
Microeconomics Instructor Miller Practice Problems International Trade and Comparative Advantage 1. Goods and services bought domestically but produced in other
D is the correct answer. Remember, whether we calculate sample SD from a sample of 1,000 or a sample of 3,000, both are estimating the same quantity- the population
Finance Practice Problems Ordinary Annuity ... Annuity Due 1 11 r nt n ... Find the future value of an annuity of $672 deposited at the beginning of each quarter for
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Which one of the following is correct? A) ν ÷ λ = c. B) ν = cλ. C) νλ = c. D) λ = c ν. E) ν + λ = .... 23) Which electron configuration represen
Put a "1" by that unit. Then ask how many of the smaller units are in the bigger unit. Put that number in front of the smaller unit. There is your conversion factor. Make sure ... 3 mg? 27. How many mL are in 0.258 L? 28. What is the density in g /mL
Momentum and Impulse Practice Problems ... A 0.105 kg hockey puck is traveling at 12 m/s when it is struck by a stick. ... coefficient of friction is 0.5,
Holt Science Spectrum. 1. Wave Speed Practice Problems. The musical note A above middle C has a frequency of 440 Hz. If the speed of sound is known to be 350 m/s, what is the wavelength of this note? 1. List the given and unknown values. Given: frequ
Reminder: These notes are meant to supplement, not replace, the laboratory manual. Aldol Condensation Notes History and Application Many aldehydes have distinctive
Solutions to Problems Note: ... cost or cash flow is one that can be realized from an alternative use of an existing asset. Here,
Date:______. Wave Speed Equation Practice Problems. The formula we are going to practice today is the wave speed equation: wave speed = wavelength* frequency v = λf. Variables, units, and symbols: Quantity. Symbol. Quantity. Term. Unit. Unit. Symbol
converges (it's a p-series with p = 2 > 1), the series ∑ n3 n5+3 also converges by the comparison test. 2. ∑. ∞ n=1. 3n. 4n+4. Answer: Notice that. 3n. 4n + 4.
Algebra Practice Problems for Precalculus and Calculus Solve the following equations for the unknown x: 1. 5 D 7x 16 2. 2x 3 D 5 x 3. 1 2.x 3/Cx D 17 C3.4 x/
Absolute and Comparative Advantage Practice Problems . For each scenario identify: Scenario 1 . Oranges harvested in one hour Orange juice squeezed in
Why can electromagnetic waves travel through a vacuum? 4. What speed do all electromagnetic waves travel at in vacuum? 5. Red light, a type of electromagnetic wave, has a wavelength of 0.0000078 meters, what is its frequency in Hz? 6. Most kitchen mi
Independent-samples t-test practice problems 1. An investigator thinks that people under the age of forty have vocabularies that are different than those of people over
Comparative Advantage Practice Problems – Remember to have the comparative advantage you must have the LOWEST OPPORTUNITY COST! Tire Changes (per hour) Oil Changes
Molarity Practice Problems 1) ... Molarity Practice Problems – Answer Key 1) How many grams of potassium carbonate are needed to make 200 mL of a 2.5 M solution?
ANOVA Practice Problems 1.
Suppose that a random sample of n = 5 was selected from the vineyard properties for sale in Sonoma County, California, in each of three years. The following data are consistent with summary information on price per acre for disease-resistant grape vineyards in Sonoma County. Carry out an ANOVA to determine whether there is evidence to support the claim that the mean price per acre for vineyard land in Sonoma County was not the same for each of the three years considered. Test at the 0.05 level and at the 0.01 level. 1996: 1997: 1998:
2.
30000 30000 40000
34000 35000 41000
36000 37000 43000
0 months 1 month 2 months 3 months
4.
40000 40000 50000
The following data on calcium content of wheat are consistent with summary quantities that appeared in the article “Mineral Contents of Cereal Grains as Affected by Storage and Insect Infestation” (Journal of Stored Products Research [1992]). Four different storage times were considered. Is there sufficient evidence to conclude that the mean calcium content is not the same for the four different storage times? Test the appropriate hypotheses at the 0.05 level.
Storage Time
3.
38000 38000 44000
Observations 58.75 58.87 59.13 62.32
57.94 56.43 60.38 58.76
58.91 56.51 58.01 60.03
56.85 57.67 59.95 59.36
55.21 59.75 59.51 59.61
57.30 58.48 60.34 61.95
Use the data below, showing a summary of highway gas mileage for several observations, to decide if the average highway gas mileage is the same for midsize cars, SUV’s, and pickup trucks. Test the appropriate hypotheses at the α = 0.01 level. n
Mean
Std. Dev.
Midsize
31
25.8
2.56
SUV’s
31
22.68
3.67
Pickups
14
21.29
2.76
To examine the effects of pets and friends in stressful situations, researchers recruited 45 people to participate in an experiment. Fifteen of the subjects were randomly assigned to each of three groups to perform a stressful task alone (control group), with a good friend present, or with their dog present. Each subject’s mean heart rate during the task was recorded. Test the appropriate hypotheses at the α = 0.05 level to decide if the mean heart rate differs between the groups. n
Mean
Std. Dev.
Control
15
82.52
9.24
Pets
15
73.48
9.97
Friends
15
91.325
8.34
5.
An investigation carried out to study the toxic effects of mercury was described in the article “Comparative Responses of the Action of Different Mercury Compounds on Barley” (International Journal of Environmental Studies [1983]). Ten different concentrations of mercury were compared with respect to their effects on average dry weight (per 100 seven-day-old seedlings). The basic experiment was replicated 4 times for a total of 40 observations. The article reported an ANOVA F statistic of 1.895. Using a significance level of 0.05, test the hypothesis that the true mean dry weight is the same for all 10 concentration levels.
6.
High productivity and carbohydrate storage ability of the Jerusalem artichoke make it a promising agricultural crop. The article “Leaf Gas Exchange and Tuber Yield in Jerusalem Artichoke Cultivars” (Field Crops Research [1991]) reported on various plant characteristics. Consider the following data on chlorophyll concentration (in grams per square meter) for four varieties of Jerusalem artichoke: n
Mean
Std. Dev.
Variety 1
5
0.3
0.12
Variety 2
5
0.24
0.089
Variety 3
4
0.41
0.1
Variety 4
6
0.33
0.054
Do the data suggest that true average chlorophyll concentration depends on the variety? State and test the appropriate hypotheses at a level of 0.05.
Solutions 1.
ANOVA Test H0:
µ1996 = µ1997 = µ1998
H a:
H0 is not true
Test Stat:
ANOVA: F = 6.834
P-Value:
0.01044
Conclude:
At the 0.01 level, there is not enough evidence to reject the null hypothesis. We cannot conclude that the mean price per acre was different in these years. At the 0.05 level, we do reject the null hypothesis and say that the mean price per acre was not the same in each year.
2.
3.
4.
Validity:
Normal populations with ≈ equal variances must be assumed.
H0:
µ 0 = µ1 = µ 2 = µ 3
H a:
H0 is not true
Test Stat:
ANOVA: F = 6.512
P-Value:
0.003
Conclude:
We reject the null hypothesis. We conclude that the mean calcium content is not the same for the four different storage times.
Validity:
Normal populations with ≈ equal variances must be assumed.
ANOVA Test
ANOVA Program H0:
µM = µS = µP
H a:
H0 is not true
Test Stat:
ANOVA: F = 13.055
P-Value:
0.0000142
Conclude:
We reject the null hypothesis. We conclude that the mean highway gas mileage is not the same for the three types of vehicles.
Validity:
Normal populations with ≈ equal variances must be assumed.
ANOVA Program H0:
µC = µ P = µ F
H a:
H0 is not true
Test Stat:
ANOVA: F = 14.08
P-Value:
0.000021
Conclude:
We reject the null hypothesis. We conclude that the mean heart rate is not the same for each of the three groups.
Validity:
Normal populations with ≈ equal variances must be assumed.
5.
6.
First of all note that df1 = 10 – 1 = 9 and df2 = 40 – 10 = 30. So we can find the P-value for this scenario by calculating Fcdf (1.895, 1e99, 9, 30) = 0.0916 . So the hypothesis test would look as follows: H0:
There is not enough evidence to reject the null hypothesis. We cannot conclude that the mean dry weight is not the same for each of the concentration levels.
Validity:
Normal populations with ≈ equal variances must be assumed.
ANOVA Program H0:
µ1 = µ 2 = µ 3 = µ 4
H a:
H0 is not true
Test Stat:
ANOVA: F = 2.6566
P-Value:
0.0836
Conclude:
There is not enough evidence to reject the null hypothesis. We cannot conclude that the mean chlorophyll concentration depends on the variety.
Validity:
Normal populations with ≈ equal variances must be assumed.
