Let X represent the standard normal random variable. The P{X > 2.07} is equal to:

Suppose that 19 measurements of the failure stress of carbon fiber specimens results in a sample mean of 562.68 MPa and sample standard deviation of 180.874 MPa and that the data is normally distributed. Calculate two-sided confidence intervals for the failure stress for the following cases:

a) 95% confidence interval for a single measurement (n = 1) of the failure stress. Assume that the population standard deviation is known to be 181 MPa.

b) 95% confidence interval for the sample mean with n = 19. Repeat for the 99% confidence interval. Assume that the population standard deviation is known to be 181 MPa

c) 95% confidence interval for the sample mean with n = 19. Repeat for the 99% confidence interval. Assume that the population standard deviation is UNKNOWN.

d) Suppose that an alternative process of producing carbon fibers results in a sample of failure stress measurements with n = 12, sample mean = 650.32 MPa and sample standard deviation of 130.470 MPa. What is the 95% confidence interval on the difference in failure stress between the two populations?

( i need Unique answer, don't copy and paste, please) (dont' use handwriting, please).

(i need references URL Link)

General Question

** How to perform logistic regression in SPSS?

Define G_N to be the game which pays the longest run of heads or tails observed in N flips of a fair coin. Let E_N be the expected value of the game G_N.

What is the difference between E₅ and E₄, to four decimal places?

Suppose that your hypotheses are H0: π = 0.25 and Ha: π < 0.25. In the context of these hypotheses, which of the following standardized statistics would provide the strongest evidence against the null hypothesis and for the alternative hypothesis? Why? A. z = –1 B. z = 0 C. z = 3 D. z = –1.80 E. z=25

4. One hundred students were interviewed. Forty–two are Monthly Active Users (MAU) of Facebook (F), and sixty–five are MAU of Snapchat(S). Thirty–four are MAU of both Facebook and Snapchat. One of the100 students is randomly selected, all 100 students having the same probability of selection (1/100).

(a) What is the probability that the student is an MAU of Facebook?

(b) What is the probability that the student is an MAU of Facebook given that the student is an MAU of Snapchat?

(c) Find Pr(S|F).

d) Express the probability in Part (b) in symbols, that is in a similar fashion to Part (c).

5. The students in Question 4 were also asked if they were MAU of Twitter. Twenty five were MAU of Twitter, including 15 who were MAU of Facebook and Twitter and 16 who were MAU of Twitter and Snapchat. Twenty four students were not MAU of any of Facebook, Snapchat or Twitter.

(a) What is the probability that a randomly selected student is an MAU of Facebook, Snapchat, and Twitter?

(b) What is the probability that a randomly selected student is an MAU of Twitter, conditional on that student being an MAU of both Facebook and Snapchat?

The data set  Roslyn in the accompanying workbook gives appraised values (In $1000’s) and size (in square feet)  for thirty houses in the Roslyn neighborhood.

a)     Use Excel’s Data Analysis ToolPak to produce output for the simple linear regression, with Valueas the response (y) variable and Size as the predictor (x) variable.

b)     Write out the equation of the regression of Value (y) on Size (x)

c)      State the numerical value of the slope of the regression line. What does it tell you in this context?

d)     State the numerical value of the standard error of the estimate? What does it tell you in this context?

e)     State the numerical value of the coefficient of determination? What does it tell you in this context?

f)      Give the 95% confidence interval for the intercept of the regression equation.   




Are there any negative numbers in this interval?   What practicalconclusion can you draw from your answer?

g)     Here is a muddled, inaccurate “explanation” of what it means to be “95% confident” in the interval for the slope.   “For 95% of samples the population slope, b,will be in the interval [0.1399, 0.2336]”
Give an accurateexplanation of “95% confidence” in this context.

h)     What practical information does the regression equation give a realtor about a 3000 square foot house ?

i)       What practical information does the regression equation give a realtor about a 30000 square foot house ?

j)       Conduct an appropriate statistical test for the significance of the regression of value on size, including a clear statement of the hypotheses.  (Note that for a Simple Linear Regression you can use either the Test for Individual Significance or the Test of Joint Significance.   You will reach identical conclusions)

k)              What practical conclusion can a realtor draw from the hypothesis test in j)?

Data:

Compute the annual standard deviation of returns for all countries from 1980 – 1981

Question 1:

1. The following table gives the frequency distribution of the number of orders received each day during the past 50 days at the office of the mail order company. Calculate the mean, mode, median, quartiles, variance and standard deviation.

b. "Fits", a designer dress retailer specialising in ladies' formal wear, is currently in the process of re-ordering a batch of formal black dinner dresses. From its records of the last 100 sales, the following statistics on the dress sizes sold were calculated:

Mean(x) = 8.75 Md= 7.5 Mo = 8

Which measure of central tendency best describes the average size of dresses sold?

c. Suppose the probability that a house of a certain type will burn down in any 12-month period is 0.004. An insurance company offers to sell the owner of such a house a $120, 000 one-year term fire-insurance policy for a premium of $690. What is the company's expected gain from such a contract?

A scientist working for a large agriculture company is interested in comparing the effect of various feed additives on the growth of chickens. Chickens were given feed supplemented with either soy, cornmeal, whey, linseed, or cricket flour. Their current diet is feed with a soy supplement. After 12 weeks on the diet, each chicken was weighed and the value (in grams) was recorded in the table below. Analyze the data to determine if there is a difference in chicken weight between the different additives and if so, which supplement is the most effective.

a. Was a pretest performed? If so, fill in the values in the table.

If not, explain why:

b. What was the conclusion of your pre-test? Do you need to transform your data? If so, fill in the transformation you used and your new critical/calculated value or new p-value.

Conclusion:

c. What are the null and alternative hypotheses for your main test?

d. Complete the ANOVA table:

e. What conclusions can you draw? Do you need to do any post-hoc testing?

f. If you need to do post-hoc testing, fill in the blank cells in the table below with: which post- hoc test you chose and the p-values for each pair of comparisons. Note: the format of the table is generic and saves space; it is not meant to imply a specific test.

g. Plot your data. Based on the results of your ANOVA and post-hoc testing, what is your biological conclusion? Use the plot to be as specific as possible.

How could an assignment problem be solved using the transportation approach? What condition will make the solution to this problem difficult?

Please give a typed answer and focus on the second part of the question.

What would be the value of your portfolio today (i.e., in 1981), if you had invested $100 in the stock market index for each country in July, 1980. Report the value of your portfolio for each country separately.

The following data is representative of that reported in an article on nitrogen emissions, with x = burner area liberation rate (MBtu/hr-ft²) and y = NO_x emission rate (ppm):

(a) Assuming that the simple linear regression model is valid, obtain the least squares estimate of the true regression line. (Round all numerical values to four decimal places.)
y =

(b) What is the estimate of expected NO_x emission rate when burner area liberation rate equals 215? (Round your answer to two decimal places.)
ppm

(c) Estimate the amount by which you expect NO_x emission rate to change when burner area liberation rate is decreased by 60. (Round your answer to two decimal places.)
ppm

(d) Would you use the estimated regression line to predict emission rate for a liberation rate of 500? Why or why not?

Yes, the data is perfectly linear, thus lending to accurate predictions.

Yes, this value is between two existing values.    

No, this value is too far away from the known values for useful extrapolation.

No, the data near this point deviates from the overall regression model.

1. Kelly and Veronica are two teachers in a math class who attend class independently of one another. For Friday classes, there is a .70 probability that kelly will come to class, while there is a .40 probability that Veronica will come to class. For a Friday class, what is the probability neither Kelly nor Veronica will be there?

2.  The weights of newborn baby twin girls have an approximately normal distribution with a mean of 8.0 pounds and a standard deviation of 1.5 pounds. A doctor tells the family that one of the baby twin girl has a weight at the 30th percentile. Which of the following is closest to this baby's weight? (show work please)

A, 7.2

B 8.5

C 7.7

D 8.9

Rejection Region

After reviewing data from a sample, an inference can be made about the population. For example,

Find a data set on the internet. Some suggested search terms: Free Data Sets, Medical Data Sets, Education Data Sets.

1. Introduce your Data Set and Cite the Source.
2. What trends do you notice in your data set?
3. Based on the trends and the history of your data set, make a claim. What kind of test (left, right, two-tailed) would you have to complete?
4. Explain the steps needed to complete the Hypothesis Test. What is needed?

After reviewing data from a sample, an inference can be made about the population. For example,

Find a data set on the internet. Some suggested search terms: Free Data Sets, Medical Data Sets, Education Data Sets.

1. Introduce your Data Set and Cite the Source.
2. What trends do you notice in your data set?
3. Based on the trends and the history of your data set, make a claim. What kind of test (left, right, two-tailed) would you have to complete?
4. Explain the steps needed to complete the Hypothesis Test. What is needed?