A sample of soy bean plots were divided into three equal groups in a completely randomized design, and each group received a different formulation of a selective weed killer (wk). The researchers measured the area of crop damage inflicted by each formulation. The aim is to choose the weed killer formulation that inflicts the least amount of crop damage. What can the researchers conclude with α = 0.05?

Conduct Tukey's Post Hoc Test for the following comparisons:
2 vs. 3: difference =  ; significant:  ---Select--- Yes No
1 vs. 3: difference =  ; significant:  ---Select--- Yes No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 2: test statistic =  ; significant:  ---Select--- Yes No
2 vs. 3: test statistic =  ; significant:  ---Select--- Yes No

The data file ExamScores shows the 40 students in a TOM 3010 course exam scores for the Midterm and Final exam. Is there statistically significant evidence to show that students score lower on their final exam than midterm exam? Provide the p-value for this analysis.

*This exercise must be done in MINITAB**

In recent years, consumers have become more safety conscious, particularly about children's products. A manufacturer of children's pajamas is looking for material that is as nonflammable as possible. In an experiment to compare a new fabric with the kind now being used, 50 piece of each kind were exposed to an open flame, and the number of seconds until the fabric burst into flames was recorded. Because the new material is much more expensive than the current material, the manufacturer will switch only if the new material can be shown to be better. On the basis of these data, what should the manufacturer do?

New Material   Old Material
15   37
21   23
14   13
27   21
20   10
17   31
18   22
24   12
16   14
15   23
18   22
15   24
20   11
24   14
14   16
17   16
19   40
40   16
16   17
29   12
14   13
23   19
15   12
24   24
13   31
25   10
14   14
13   11
17   12
15   10
19   15
20   11
28   32
22   21
32   16
17   12
23   32
15   13
16   23
32   19
13   23
13   16
32   13
17   14
22   32
14   28
24   27
20   22
19   13
22   14

List and discuss the steps involved in formulating LP models? How might this differ for ILP models?

Sixty-five percent of registered voters, voted in the last presidential election. A researcher surveyed 1200 registered voters and found that 700 voted at the midterm elections. Can the researcher say that the proportion of the midterm election voters is different from the presidential elections at a 2% level of significance?

a) State the distribution you will use and why?

b) State the null and Alternate Hypothesis. Identify the claim.

c)Find the critical value.

d)find the test statistic and the P-Value

e) Make a decision. Write a conclusion.

The data table below gives the diameter and age of 27 trees that were cut down to make open space for a playground. Diameter (inches) 1.8 1.8 2.2 4.4 6.6 4.4 7.7 10.8 Age (years) 4 Diameter (inches) 10.3 14.3 13.2 9.9 13.2 15.4 17.6 14.3 15.4 11.0 15.4 16.5 16.5 Age (years) 23 25 28 29 30 30 10 10 12 13 14 16 18 20 34 35 38 38 40 5.5 9.9 10.1 12.1 12.8

Create a linear model for solving the slope and intercept of the best fitting straight line by hand. Show all work

Rothamsted Experimental Station (England) has studied wheat production since 1852. Each year, many small plots of equal size but different soil/fertilizer conditions are planted with wheat. At the end of the growing season, the yield (in pounds) of the wheat on the plot is measured. For a random sample of years, one plot gave the following annual wheat production (in pounds).

Use a calculator to verify that, for this plot, the sample variance is s² ≈ 0.307.

Another random sample of years for a second plot gave the following annual wheat production (in pounds).

Use a calculator to verify that the sample variance for this plot is s² ≈ 0.096.

Test the claim that the population variance of annual wheat production for the first plot is larger than that for the second plot. Use a 1% level of significance.

(a) What is the level of significance?

State the null and alternate hypotheses.

H_o: σ₁² = σ₂²; H₁: σ₁² > σ₂²H_o: σ₁² > σ₂²; H₁: σ₁² = σ₂²     H_o: σ₂² = σ₁²; H₁: σ₂² > σ₁²H_o: σ₁² = σ₂²; H₁: σ₁² ≠ σ₂²

(b) Find the value of the sample F statistic. (Use 2 decimal places.)


What are the degrees of freedom?

What assumptions are you making about the original distribution?

The populations follow independent normal distributions. We have random samples from each population. The populations follow dependent normal distributions. We have random samples from each population.     The populations follow independent normal distributions. The populations follow independent chi-square distributions. We have random samples from each population.

(c) Find or estimate the P-value of the sample test statistic. (Use 4 decimal places.)

p-value > 0.100 0.050 < p-value < 0.100     0.025 < p-value < 0.050 0.010 < p-value < 0.025 0.001 < p-value < 0.010 p-value < 0.001

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.     At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(e) Interpret your conclusion in the context of the application.

Fail to reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production is greater in the first plot. Reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production is greater in the first plot.     Reject the null hypothesis, there is sufficient evidence that the variance in annual wheat production is greater in the first plot. Fail to reject the null hypothesis, there is insufficient evidence that the variance in annual wheat production is greater in the first plot.

Data 13A is Ho: μx = 80.0 σx = 20.0 Ha: μx ≠ 80.0 n =100, In regard to DATA 13A... (a) If α = .05 and μtrue = 84.0, what is β? What is the power of the test? (b) If α = .05 and μtrue = 84.0, but Ha:ux > 80.0 what is β? What is the power of the test?

A wildlife biologist examines frogs for a genetic trait that may possibly be linked to industrial toxins in the environment. This trait is usually found in 1 of every 7 frogs, so the prevalence is 0.143. A sample of 85 frogs are collected and examined. (Enter all probabilities with 3 decimal points.)

The expected number of frogs in the sample with this trait is (enter with 2 decimal points) 12.15

What is the probability that this trait is in none of the sampled frogs? P(X=0) = 0.000

What is the probability that no more than 4 frogs in the sample have this trait? P(X =< 4) = 0.004

What is the probability that 7 or 8 frogs in the sample have this trait?

What is the probability that at least 7 frogs in the sample have this trait?

1. In the experiment of rolling a balanced die twice. Let X be the minimum of the two numbers obtained and Y be value of the first roll minus the value of the second roll. Determine the probability mass functions and cumulative distribution functions of X and Y, and sketch their graphs

please also solve probability for Y

Question 5: Data on the total tobacco exposure time (in seconds) for G-rated animated films with tobacco use released between 1937 and 1997 produced by Walt Disney, Inc. are as follows:

223 176 548 37 158 51 299 37 11 165 74 92 6 23 206 9

Similar data for G-rated animated films with tobacco use produced by MGM/United Artists, Warner Brothers, Universal, and Twentieth Century Fox are as follows:

205 162 6 1 117 5 91 155 24 55 17

(a) . Construct a back-to-back stem-and-leaf plot to compare the two exposure-time distributions. Use hundreds for stems and tens (truncated) for leaves. Divide each stem into a ”Low” and ”High” part.

(b) . Compare the two exposure-time distributions with respect to shape, centre, spread and outliers

A bottling plant needs to know how to report its success in filling 2-liter (2 L) bottles. From previous work, they know that the population standard deviation is ±0.05 L.

a. For this part, assume an “infinite” population. They sample 35 bottles and obtain a sample mean of 1.99 L. For 95% confidence, what is the estimate of the range of the population mean?
b. For this part, assume an “infinite” population. If they desire an estimate of the interval for the population mean that is ±0.01 L, how many samples do they need to examine (with 95% confidence).

Two people are playing an exciting game in which they take turns removing marbles from a bag. At the beginning of the game, this bag contains some red marbles and some blue marbles. The bag is transparent so at any time during the game, the players know exactly how many red and how many blue marbles are in the bag.

The players alternate taking turns. On a player’s turn, he or she must remove some marbles from the bag. The player chooses which marbles to remove, under the condition that he or she remove at least one marble and the marbles removed in a single turn are all the same color. The player to remove the last marble from the bag during his or her turn wins.

Assume that player 1 is playing the game with player 2, and player 1 makes the first move. If you were player 1, what optimal strategy could you use to play this game? Under what starting conditions would this optimal strategy guarantee a win, and why? What can you say about the outcome of the game if these starting conditions are not met?

(Hint: Try thinking of an invariant you could maintain during certain points of the game)

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.88 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.) lower limit $ upper limit $ margin of error $

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.33 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.) farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.) lower limit $ upper limit $ margin of error $

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.† Suppose a small group of 19 Allen's hummingbirds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with σ = 0.32 gram.

(a) Find an 80% confidence interval for the average weights of Allen's hummingbirds in the study region. What is the margin of error? (Round your answers to three decimal places.)

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is known uniform distribution of weights normal distribution of weights n is large σ is unknown

(c) Interpret your results in the context of this problem.

The probability to the true average weight of Allen's hummingbirds is equal to the sample mean.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.80.    

There is an 80% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

There is a 20% chance that the interval is one of the intervals containing the true average weight of Allen's hummingbirds in this region.

The probability that this interval contains the true average weight of Allen's hummingbirds is 0.20.

(d) Find the sample size necessary for an 80% confidence level with a maximal margin of error E = 0.15 for the mean weights of the hummingbirds. (Round up to the nearest whole number.)
                            hummingbirds