When one company (A) buys another company(B), some workers of company B are terminated. Terminated workers get severance pay. To be fair, company A fixes the severance payment to company B workers as equivalent to company A workers who were terminated in the last one year. A 36-year-old Mohammed, worked for company B for the last 10 years earning 32000 per year, was terminated with a severance pay of 5 weeks of salary. Bill smith complained that this is unfair that someone with the same credentials worked in company A received more. You are called in to settle the dispute. You are told that severance is determined by three factors; age, length of service with the company and the pay. You have randomly taken a sample of 40 employees of company A terminated last year. You recorded

Number of weeks of severance pay

Age of employee

Number of years with the company

Annual pay in 1000s

2. How much variance is not explained by the model? Test the validity of the models that X predict Y (provide hypotheses, decision, conclusion and conclusion in the business context)

1An agronomist was interested in finding out the amount of potassium in corn leaves, not including the stems, after four different fertilizers had been used in a field of corn

A. If 5 plots of corn were used per fertilizer in a completely randomized manner, show the layout of an experiment.

B. If in the 5 plots per fertilizer, 2 stalks of corn per plot were to be sampled from the experimental area, show the Anova table and state the assumptions necessary to test the effects of fertilizer.

C. Comment on this design (in part(B)) and analysis.

* part A, B & C please with as much detail as possible

What is the difference between the scales of measurement? Specifically Ordinal, Interval and Ratio scales of measurement because they are all very similar. Please provide good examples and explanation so I can understand the difference and not be confused when trying to determine/ solve for a variable.

Example:

Each voter was asked to rate their support for the current government on a scale from 0-100 (zero indicates no support whatsoever, while 100 indicates fully supporting the current government).

Voter support is the dependent variable but is it ordinal or interval scale of measurement?

A new thermostat has been engineered for the frozen food cases in large supermarkets. Both the old and new thermostats hold temperatures at an average of 25°F. However, it is hoped that the new thermostat might be more dependable in the sense that it will hold temperatures closer to 25°F. One frozen food case was equipped with the new thermostat, and a random sample of 26 temperature readings gave a sample variance of 4.4. Another similar frozen food case was equipped with the old thermostat, and a random sample of 19 temperature readings gave a sample variance of 12.8. Test the claim that the population variance of the new thermostat temperature readings is smaller than that for the old thermostat. Use a 5% level of significance. How could your test conclusion relate to the question regarding the dependability of the temperature readings? (Let population 1 refer to data from the old thermostat.) (a) What is the level of significance? State the null and alternate hypotheses. H0: σ12 = σ22; H1: σ12 ≠ σ22 H0: σ12 > σ22; H1: σ12 = σ22 H0: σ12 = σ22; H1: σ12 > σ22 H0: σ12 = σ22; H1: σ12 < σ22 (b) Find the value of the sample F statistic. (Round your answer to two decimal places.) What are the degrees of freedom? dfN = dfD = What assumptions are you making about the original distribution? The populations follow independent chi-square distributions. We have random samples from each population. The populations follow independent normal distributions. The populations follow dependent normal distributions. We have random samples from each population. The populations follow independent normal distributions. We have random samples from each population. (c) Find or estimate the P-value of the sample test statistic. (Round your answer to four 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 = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Reject the null hypothesis, there is sufficient evidence that the population variance is smaller in the new thermostat temperature readings. Fail to reject the null hypothesis, there is insufficient evidence that the population variance is smaller in the new thermostat temperature readings. Reject the null hypothesis, there is insufficient evidence that the population variance is smaller in the new thermostat temperature readings. Fail to reject the null hypothesis, there is sufficient evidence that the population variance is smaller in the new thermostat temperature readings.

A test has an overall mean of 150 and a standard deviation of 8.50. The distribution of scores for each sub-set is often closely approximated by the normal curve. What percentage of students will score lower than 142 or better than 158?

1. The table below shows the data on temperature (℉) reached on a given day and the number of cans of soft drinks sold from a particular vending machine in front of a grocery store. Temperature 70 75 80 90 93 98 72 75 95 98 91 83 Quantity 30 31 40 52 57 59 33 38 45 53 62 45 a. Draw a scatterplot for the data. b. Compute the least squares regression line ?̂. c. Interpret the slope and y-intercept if appropriate. d. Compute the linear correlation coefficient ? between temperature and the number of soft drinks sold. Does a linear relation exist between temperature and the number of soft drinks sold? e. How many cans of soft drinks can be sold at a temperature of 62℉? Round your answer to the nearest can.

Suppose you have been building a model using the k-means clustering algorithm and you keep finding that a certain variable is essentially ignored by the model (in other words, the variable is very similarly distributed across all clusters). Describe a method that can be used to exaggerate or minimize the impact of a variable when using k-means clustering. Why does this method work?

no additional info available, predictive analysis

A $1 coin is tossed until a head appears, and let N be the total number of times that the $1 coin is tossed. A $5 coin is then tossed N times. Let X count the number of heads appearing on the tosses of the $5 coin. Determine P(X = 0) and P(X = 1).

An engineer is studying the effect of cutting speed on the rate of metal removal in a machining operation. However, the rate of metal removal is also related to the hardness of the test specimen. Five observations are taken at each cutting speed. The amount of metal removed y and the hardness of the specimen x are shown below in the format of a data file. Column 1 has treatment (1 for cutting speed 1000, 2 for cutting speed 1200, 3 for cutting speed 1400), column 2 has x=hardness, column 3 has y=amount of metal removed.
1 125 77.4
1 120 68.4
1 140 90.4
1 150 97.9
1 136 87.6
2 133 85.4
2 140 94.4
2 125 74
2 120 64.8
2 165 112.1
3 130 79.6
3 175 117.6
3 132 82.3
3 141 91.9
3 124 72.9


Do an analysis of these data and include the following.
1. A scatterplot of the ys versus the xs, using different symbols (or colours) to distinguish the points corresponding to different cutting speeds. Do the ys appear to be related to the xs? Include regression lines of y versus x for each cutting speed. Does it seem reasonable to believe that these three lines have the same slope?
2. An ANCOVA table.
3. An ANOVA table based on the ys, disregarding the xs, to determine whether there are differences in the (mean) amount of metal removed for different cutting speeds. Comment on differences with part (2).

You will be asked a few questions concerning the analysis.

Please use 3 decimal places for the answers below which are not integer-valued.


Part a)
The type II SS for cutting speed (treatment) is______ and its degree of freedom is______    

Part b)
The MSE for ancova is:______    and its degree of freedom is______    

Part c)
The appropriate F ratio for cutting speed is:
______  ​

Part d)
What is the estimate slope for x=hardness?
______  

One in four adults is currently on a diet. You randomly select ten adults and ask them if they are currently on a diet. Find the probability that the number who say they are currently on a diet is (a) exactly three, (b) at least three, (c) more then three, (d) at most four, and (e) less than six.

The British Department of Transportation studied to see if people avoid driving on Friday the 13th.   They did a traffic count on a Friday and then again on a Friday the 13th at the same two locations ("Friday the 13th," 2013). The data for each location on the two different dates is in table #9.2.6. Estimate the mean difference in traffic count between the 6th and the 13th using a 90% level.
Table #9.2.6: Traffic Count
Dates 6th 13th
1990, July 139246 138548
1990, July 134012 132908
1991, September 137055 136018
1991, September 133732 131843
1991, December 123552 121641
1991, December 121139 118723
1992, March 128293 125532
1992, March 124631 120249
1992, November 124609 122770
1992, November 117584 117263

A marketing research firm wishes to compare the prices charged by two supermarket chains—Miller’s and Albert’s. The research firm, using a standardized one-week shopping plan (grocery list), makes identical purchases at 10 of each chain’s stores. The stores for each chain are randomly selected, and all purchases are made during a single week. It is found that the mean and the standard deviation of the shopping expenses at the 10 Miller’s stores are x1¯¯¯¯?=?$114.14x1¯?=?$114.14 and s₁= 1.12. It is also found that the mean and the standard deviation of the shopping expenses at the 10 Albert’s stores are x2¯¯¯¯?=?$113.14x2¯?=?$113.14 and s₂= 1.67.

(a) Calculate the value of the test statistic. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Test statistic          

(b) Calculate the critical value. (Round your answer to 2 decimal places.)

Critical value          

(c) At the 0.02 significance level, what it the conclusion?

Suppose two independent random samples of sizes n₁ = 9 and n₂ = 7 that have been taken from two normally distributed populations having variances σ12σ21 and σ22σ22 give sample variances of s₁² = 117 and s₂² = 19.

(a) Test H₀: σ12σ21 = σ22σ22 versus H_a: σ12σ21 ≠≠ σ22σ22 with σσ = .05. What do you conclude? (Round your answers to 2 decimal places.)

(b) Test H₀: σ12σ21< σ22σ22versus H_a: σ12σ21 > σ22σ22 with σσ = .05. What do you conclude? (Round your answers to 2 decimal places.)

The correlation coefficient r is a sample statistic. What does it tell us about the value of the population correlation coefficient ρ (Greek letter rho)? You do not know how to build the formal structure of hypothesis tests of ρ yet. However, there is a quick way to determine if the sample evidence based on ρ is strong enough to conclude that there is some population correlation between the variables. In other words, we can use the value of r to determine if ρ ≠ 0. We do this by comparing the value |r| to an entry in the correlation table. The value of α in the table gives us the probability of concluding that ρ ≠ 0 when, in fact, ρ = 0 and there is no population correlation. We have two choices for α: α = 0.05 or α = 0.01. (a) Look at the data below regarding the variables x = age of a Shetland pony and y = weight of that pony. Is the value of |r| large enough to conclude that weight and age of Shetland ponies are correlated? Use α = 0.05. (Use 3 decimal places.) x 3 6 12 21 24 y 60 95 140 190 172 r Incorrect: Your answer is incorrect. critical r Incorrect: Your answer is incorrect. Conclusion Reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. Reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. Fail to reject the null hypothesis, there is insufficient evidence to show that age and weight of Shetland ponies are correlated. Fail to reject the null hypothesis, there is sufficient evidence to show that age and weight of Shetland ponies are correlated. Correct: Your answer is correct. (b) Look at the data below regarding the variables x = lowest barometric pressure as a cyclone approaches and y = maximum wind speed of the cyclone. Is the value of |r| large enough to conclude that lowest barometric pressure and wind speed of a cyclone are correlated? Use α = 0.01. (Use 3 decimal places.) x 1004 975 992 935 970 924 y 40 100 65 145 65 146 r critical r Incorrect: Your answer is incorrect. Conclusion Reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. Reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. Fail to reject the null hypothesis, there is insufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated. Fail to reject the null hypothesis, there is sufficient evidence to show that lowest barometric pressure and maximum wind speed for cyclones are correlated.

1.

Suppose that

Superman is the favorite hero of

3

5%

of

all DC Comics fans, Batman is the

favorite of 26% of fans, Wonder Woman is the favorite of 19%, Green Lantern is the favorite

of 12%, and the

Flash is the favorite of all the rest of fans

.

a)

If a

DC Comics fan

is selected at random, what is the

probability that

:

i.

T

he Flash is that person’s favorite superhero

?

ii.

T

he person’s favorite superhero is Batman or Wonder Woman?

iii.

T

he person’s

favorite superhero is not Superman

?

b)

If you were to randomly select

five

DC Comics fans

, what is the probability that:

i.

Batman

is the favorite superhero of all five people

?

2

ii.

No

ne of the

five

people

identify Green Lantern as their favorite superhero

?

iii.

All five people identify

Green Lantern

as their favorite superhero

or

all five identify

Wonder Woman

as their favorite

?

iv.

N

ot

all

five

people identify

the Flash

as their favorite superhero

?

v.

Superman is the favorite superhero of

at least

one of the

five

people

?