A fashion designer was looking to improve her brand's most recent collection of clothes by adding a casual line to the brand as well. The casual line would include shorts, t-shirts, and sandals. The designer sampled seven potential customers to find the average price they were willing to pay for their favorite brand of shorts. The results are as follows. 21, 24, 26, 28, 27, 30, 12

1. Calculate the margin of error for a 95% confidence interval for the population mean. (Use a table or technology. Round your answer to three decimal places.)

2. Calculate the 95% confidence interval for the population mean. (Use a table or technology. Round your answers to three decimal places.)

Consider the variables y, x1 and x5 from Table B.2 of page 555 in the textbook, regarding Solar Thermal Energy Test Data. 1. Construct a normal probability plot of the residuals. does there seem to be any problem with the normality assumption? 2. Construct and interpret a plot of the residuals versus the predicted response. 3. Construct plots of the residuals versus each of the regressor variables. Do these plots imply that regressor is correctly specified? 4. Construct partial regression plots of residuals versus regressors from part c. Discuss the type of information provided by these plots. 5. Compute the studentized residuals and the R−student residuals for this model. What information is conveyed by these scaled residuals?

needs R coding guidance as well as results

A simple Statistic question by using R,

If I have two set of mean proportion data, what test should I use?

such as,

 [1] 0.7652632 0.7555354 0.7602588 0.7594096 0.7497992 0.5532588 0.7595661 0.6911504
 [9] 0.5964602 0.6369565 0.7355828 0.7346225 0.5913793 0.6499079 0.6327273 0.6091873
[17] 0.6306122 0.5960784 0.5492918 0.6785714 0.5014787 0.5484848 0.5645403 0.6731343
[25] 0.6208191 0.6087248 0.6045045 0.7743390 0.5275862 0.5731278

 [1] 0.6564195 0.5928482 0.6806709 0.5546422 0.5438393 0.5906535 0.6764637 0.6487188
 [9] 0.5901547 0.6626735 0.5955325 0.7462415 0.5971111 0.5731504 0.6334729 0.6124653
[17] 0.6224686 0.5549067 0.6348427 0.6265627 0.5981283 0.5981034 0.6374002 0.6400281
[25] 0.7951639 0.7002149 0.7037493 0.6003284 0.6924103 0.7035969 0.5354807 0.6441660
[33] 0.5850962 0.6178425 0.5608873 0.5515344 0.6188244 0.5907285 0.6370565 0.5762872
[41] 0.6229073 0.6044919 0.6150885 0.5970907 0.6029415 0.6050567 0.5793054 0.4934299
[49] 0.5536594 0.5976290 0.6712677 0.6082890 0.6201184 0.5589970 0.5568638 0.5559723
[57] 0.6501545 0.5920379 0.5645405 0.5882715 0.5729236 0.6249503 0.6778542 0.5434909
[65] 0.5683645 0.6241660 0.6587552 0.5916995 0.5645792 0.6114187 0.5738135 0.6521985
[73] 0.6564125 0.7089936 0.6521985 0.6364080 0.6445784 0.5712456 0.5789808 0.5493933

and please interpret their p value

One of Mary’s investments is going to mature, and she wants to determine how to invest the proceeds of $50,000. Mary is considering three new investments: a business startup fund (BSF), a one-year certificate of deposit (CD) with a guarantee of 4.5% return, or a communication technology stock called New 5 G Technology(N5G).

Mary estimates the return on BSF as 15%, 9%, -3% or -12%, and the return on N5G as 33%, 28%, -13% or -22%, depending on whether market conditions are excellent, good, average, or poor, respectively. Mary also has been collecting financial market information daily and estimates the probabilities of an excellent, good, average, and poor market to be 0.23, 0.20, 0.47, and 0.10, respectively.

(B-1) Construct a payoff matrix (in dollars) for this problem.

(B-2) What decision should be made according to Expected Value Approach?

(B-3) Create a regret table and explain what decision should be made according to Minimax Regret Approach.

(B-4) What is the EVPI?

Scores of an IQ test have a​ bell-shaped distribution with a mean of 100 and a standard deviation of 10. Use the empirical rule to determine the following

a) What percentage of people has an IQ score between 70 and 130​?

​(b) What percentage of people has an IQ score less than 90 or greater than 110​?

​(c) What percentage of people has an IQ score greater than 120​?

A service process has three serial stages. The defect percentage at stage one is 16%. The defect percentage at stage two is 13%. And, the defect percentage at stage three is 10%. Use 3 decimals for probabilities in the following situations. (a)[2] Situation A: the connection logic of the three stages is that a good overall outcome only happens if all three stages individually have good outcomes. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. (b)[2] Situation B: the connection logic of the three stages is that a good overall outcome happens when at least one stage has good outcome. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. (c)[3] Situation C: the connection logic of the three stages is that a good overall outcome happens when at least two stages individually have good outcomes. Draw the event tree for this situation. Calculate the probability of defective overall outcomes and the probability of good overall outcomes. (d)[3] Give some possible real‐life processes for the three situations above.

According to the Current Results website, the state of California has a mean annual rainfall of 23 inches, whereas the state of New York has a mean annual rainfall of 45 inches. Assume that the standard deviation for both states is 3 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken. Use z-table. a. Show the probability distribution of the sample mean annual rainfall for California. This is a graph of a normal distribution with E(-/x) and 0x (to 4 decimals). b. What is the probability that the sample mean is within 1 inch of the population mean for California? (to 4 decimals) c. What is the probability that the sample mean is within 1 inch of the population mean for New York? (to 4 decimals) d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why? The probability of being within inch is for New York in part (c) because the sample size is

ABC Apartments is a 300-unit complex near Fairway University that attracts mostly university students. The manager has collected the following data and wants to project the number of units leased in Semester 9 using simple linear regression. Here is the information that has been collected:

In answering these questions, you must identify and use the correct independent and dependent variables.

a) The apartment manager wants to forecast the Number of Units Leased as a function of time. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9?

b) Suppose the manager believes that the Number of Units Leased is a function only of University Enrollment. It is believed that there will be a one semester lag between the enrollment and the units leased. In other words, the number of units leased in a semester is a function of the university enrollment in the prior semester. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9?

c) Suppose the manager believes that the Number of Units Leased is a function only of the Average Lease Price for that semester. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9 if the average lease price for that semester is $450?

d) Considering the strength of each of the relationships that you found in parts a) through c), would you use any of these to forecast the Number of Units Leased for Semester 9? Explain your answer.

Cox Electric makes electronic components and has estimated the following for a new design of one of its products:

Fixed Cost = $3,000

Material cost per unit = $0.15

Labor cost per unit = $0.10

Revenue per unit = $0.65

Production Volume = 12,000
Per-unit material and labor cost together make up the variable cost per unit. Assuming that Cox Electric sells all it produces, build a spreadsheet model that calculates the profit by subtracting the fixed cost and total variable cost from total revenue, and answer the following questions.

An automatic filling machine is used to fill bottles with liquid detergent. A random sample of 20 bottles results in a sample variance of fill volume of s^2 = 0.0153 (fluid oz)^2 . Assume that the fill volume is approximately normal. Compute a 95% upper confidence bound for the population standard deviation. Provide practical interpretation of the result.

Need Linear Regression Analysis done for the following data:

1. An article from an Environmental Engineering journal reported the results of a study on the occurrence
of sodium and chloride on the surface of water currents in Rhode Island. The following data presents
the concentration of chloride designated ? (in milligrams per liter) and the taxiway area in the basin
as ? (in percentage).
? 4.4 6.6 9.7 10.6 10.8 10.9
? 0.19 0.15 0.57 0.70 0.67 0.63
? 11.8 12.1 14.3 14.7 15.0 17.3
? 0.47 0.70 0.60 0.78 0.81 0.78
? 19.2 23.1 27.4 27.7 31.8 39.5
? 0.69 1.30 1.05 1.06 1.74 1.62
a) Draw a scatter diagram of the data. Does a simple linear model look appropriate?
b) Adjust the simple linear regression using the least squares method. Find the
estimate of σ
two
.
c) Estimate the average concentration of chloride for the basin that has 1% taxi area.
d) Find the adjusted value corresponding to ? = 0.47 and the associated residual.

2. Consider the data from exercise # 1 where ? is equal to the concentration of chloride on the surfaces of
current and ? is the taxi area.
a) Test the hypothesis Ho: β1 = 0 versus H1: β1 ≠ 0 using the analysis of variance procedure
with α = 0.01.
b) Find the p-value for the test of part a.
c) Estimate the standard errors for β
1 and β
0

Explore the relationship between the selling price appraised value and the selling price.

(Draw a scatterplot and then do simple regression.)

. Draw a scatterplot first. What is the regression equation for Selling Price based on Appraised Value?

2. For which of the remaining variables is the relationship with the home's selling price Stronger?

3. Find a regression equation that takes into account ALL the variables in the data set.

4. What percent of a home's selling price is associated with all these v

There are 7 balls numbered 1 through 7 placed in a bucket. What is the probability of reaching into the bucket and randomly drawing two balls numbered 6 and 3 without replacement, in that order? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.

Consider a binomial experiment with 15 trials and probability 0.55 of success on a single trial.

(a) Use the binomial distribution to find the probability of exactly 10 successes. (Round your answer to three decimal places.)


(b) Use the normal distribution to approximate the probability of exactly 10 successes. (Round your answer to three decimal places.)


(c) Compare the results of parts (a) and (b).

These results are fairly different.These results are almost exactly the same.