One hundred blood samples were taken from 100 individuals. All of the blood samples were run through two machines to determine if the machines were testing samples appropriately. We expect that both machines should yield similar results. Below are the results of the analysis. Assume there are 100 sample and they are normal. Are the two machines similar? Should we check into whether one machine should be replaced? Show all of your work.

Use the given statistics to complete parts​ (a) and​ (b). Assume that the populations are normally distributed.

Population 1 Population 2

n=24 n=17

x=47.4 x=42.2

s=6.2 s=9.7

​(a) Test whether μ1>μ2 at the α=0.05 level of significance for the given sample data. ​

(b) Construct a 99% confidence interval about μ1−μ2.

Scores on an aptitude test are known to follow a normal distribution with a standard deviation of 32.4 points. A random sample of 12 test scores had a mean score of 189.7 points. Based on the sample results, a confidence interval for the population mean is found extending from 171.4 to 208 points. Find the confidence level of this interval.

Margin of Error (ME)= ?

Z-Score (Z-a/2)= ?

Confidence Level= ?

The intelligence quotients of 400 children have a mean value of 100 and a standard deviation of 14. Assuming that I.Q.’s are normally distributed, determine the number of children likely to have I.Q.’s of between

(a) 80 and 90,

(b) 90 and 110 and

(c) 110 and 130.

Suppose you start up a company that has the developed a drug that is supposed to increase IQ.   You know that the standard deviation of IQ in the general population is 45. You test your drugs on 36 patients and obtain I mean IQ of 103. Using a alpha value of 0.05, is this IQ significantly different from the population mean of 100?

Which hypothesis test is appropriate? Match. THESE are all connected. AN)VA, chi square, f test for two variances, one sample left tailed t, one sampled right tailed t

1.Research shows that there is one critical dimension on yo-yos. If the dimension falls within a certain range of values, it drastically improves yo-yo performance. You have some ideas for manufacturing processes which will keep the mean value of that dimension the same, while potentially reducing the standard deviation. You want to compare these processes to the current process.

2.Research shows that there is one critical dimension on yo-yos. If the dimension falls within a certain range of values, it drastically improves yo-yo performance. You have some ideas for manufacturing processes which will keep the mean value of that dimension the same, while potentially reducing the standard deviation. You want to compare these processes to the current process.

3. You poll people across the USA (across 5 regions), asking their favorite brand of soda (coca-cola, diet-coke, pepsi, diet-pepsi etc.). You want to understand if soda preference is independent of region.

4.You want to understand if the mean weight of 10-year-old boys in your town is greater than the national average.

5.You own a major corporation with franchise locations. There are five franchise owners, which each own more than 100 stores. You want to understand if there is a statistically significant difference in mean profit across these stores by franchise owners.

There are three hospitals in the Tulsa, Oklahoma, area. The following data show the number of outpatient surgeries performed on Monday, Tuesday, Wednesday, Thursday, and Friday at each hospital last week. At the 0.01 significance level, can we conclude there is a difference in the mean number of surgeries performed by hospital or by day of the week?

State the decision rule for 0.01 significance level. (Round your answers to 2 decimal places.)

For Treatment:

For blocks:

Complete the ANOVA table. (Round your SS, MS and F to 2 decimal places.)

Xn are independent random variables and each one of them has a normal distribution with mean 0 and variance 1

what is the distribution of X-bar if n=9

what is the probability of X-bar =<3 if n=9

4. Consider two stocks with returns ?_A and ?_B with the following properties. ?_A takes values -10 and +20 with probabilities 1/2. ?_B takes value -20 with probability 1/3 and +50 with probability 2/3. ????(?_A,?_B) = ? (some number between -1 and 1). Answer the following questions

   1. (a) Express C??(?_A,?_B) as a function of ?

   2. (b) Calculate the expected return of a portfolio that contains share ? of stock ? and

      share 1 − ? of stock ?. Your answer should be a function of ?

   3. (c) Calculate the variance of the portfolio from part ? (Hint: returns are now potentially dependent)

   4. (d) What value of ?* minimizes the variance of the portfolio? Your answer should be a function of ?, denoted by ?*(?).

5. (e) For what range of values for ? is your ?*(?) ≤ 1? What is the solution to the above problem if ? is outside of that range? (Hint: draw a graph and nd ?* ∈ [0, 1] that minimizes variance)

6. (f) Is ?*(?) increasing or decreading? (Hint: take the derivative with respect to ?)

7. (g) Which ? would the investor prefer to have, positive or negative? What is the intuition for that result?

3. There is one 1$ bill and one 5$ bill in your left pocket and the same in your right pocket. You move one bill from the left pocket to the right pocket. After that you take the remaining bill from the left pocket and one of the bills at random from the right pocket. Let ? denote the amount of money that you take from the left pocket and ? denote the amount of money that you take from the right pocket. Answer the following questions.

(a) Calculate the joint PMF of ? and ? and the marginal PMF( Probability mass function)-s

(b) Are ? and ? independent?

(c) Find C??(?, ? ) and C???(?, ? )

(d) Find V??(? + ? )

(e) Let ? be the total amount of money that you take from your pockets. Find the PMF of ?, its mean and variance

(f) Find C??(?, ?) and C???(?, ?)

4. Flip a fair coin 4 times. Let ? and ? denote the number of heads and tails correspondingly.

   (a) What is the distribution of ?? What is the distribution of ? ?

5. (b) Find the joint PMF. Are ? and ? independent?

   (c) Calculate ?(? ?) and ?(X≠?)(d) Calculate C??(?, ? ) and C???(?, ? )

Consider a hyper geometric probability distribution with n=7, R= 8 and N=17

a) calculate P(x =5)

b) calculate P(x=4)

c) calculate P(x <=1)

d) calculate the mean and strandard deviation of this distribution

The number of hits to a website follows a Poisson process. Hits occur at the rate of 0.8 per minute between​ 7:00 P.M. and 9​:00 P.M. Given below are three scenarios for the number of hits to the website. Compute the probability of each scenario between 8:39 P.M. and 8​:47 P.M. Interpret each result.

​(a) exactly seven P(7)=

(Round to four decimal places as​ needed.)

​(b) fewer than seven

​(c) at least seven

​

​(Round to four decimal places as​ needed.)

The following data represent a company's yearly sales volume and its advertising expenditure over a period of 5 years.

(Y) Sales in Advertising (X) Millions of Dollars in ($10,000)

15 32

16 33

18 35

17 34

16 36

(a) Develop a scatter diagram of sales versus advertising and explain what it shows regarding the relationship between sales and advertising.

(b) Use the method of least squares to compute an estimated regression line between sales and advertising by computing b0 and b1.

(c) If the company's advertising expenditure is $400,000, what are the predicted sales? Give the answer in dollars.

(d) What does the slope of the estimated regression line indicate?