Question 3: Consider a 25 factorial design.
(a) How many factors and levels are considered in this factorial experiment?
(b) Show all the 32 treatment combinations using a, b, c, d, and e.
(c) Suppose you are not able to complete all 32 experiments in a day but you believe 16 experiments can be done in a day. How many blocks do you need under this situation?
(d) Revisiting part (c), which interaction effect would be confounded with the blocks? Using the sign method, assign optimal treatment combinations to each block.
(e) Revisiting part (c), now assign optimal treatment combinations to each block by using the defining contrast method. Note that the optimal treatment combinations you have found in parts (d) and (e) should be the same.

Given the joint probability density function f(x ,y )=k (xy+ 1) for 0<x <1--and--0<y<1 , find the correlation--ROW p (X,Y) .

A random sample of n₁ = 16 communities in western Kansas gave the following information for people under 25 years of age.

x₁: Rate of hay fever per 1000 population for people under 25

A random sample of n₂ = 14 regions in western Kansas gave the following information for people over 50 years old.

x₂: Rate of hay fever per 1000 population for people over 50

What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate. (Test the difference μ₁ − μ₂. Do not use rounded values. Round your answer to three decimal places.)

The accompanying data table lists measured voltage amounts supplied directly to a​ family's home. The power supply company states that it has a target power supply of 120 volts. Using those home voltage​ amounts, test the claim that the mean is 120 volts. Use a 0.01 significance level.

Day   Volts
1   123.9
2   123.9
3   123.9
4   123.9
5   123.4
6   123.3
7   123.3
8   123.6
9   123.5
10   124.4
11   123.5
12   123.7
13   124.2
14   123.7
15   123.9
16   124.0
17   124.2
18   123.9
19   123.8
20   123.8
21   124.0
22   123.9
23   123.6
24   123.9
25   123.4
26   123.4
27   123.4
28   123.4
29   123.3
30   123.5
31   123.5
32   123.6
33   123.6
34   123.9
35   123.9
36   123.8
37   123.9
38   123.7
39   123.8
40   123.8

1. Calculate the test statistic

2. What is the range of P-value

a. P-value<0.01

b. P-value > 0.20

c. 0.025 < P-value < 0.05

d. 0.05 < P-value < 0.10

e. 0.10 < P-value < 0.20

f. 0.01 < P-value < 0.025

3. Identify the critical value(s)

A​ government's department of transportation reported that in​ 2009, airline A led all domestic airlines in​ on-time arrivals for domestic​ flights, with a rate of 82.9%.

Complete parts a through e below.

a.What is the probability that in the next six​ flights, exactly four flights will be on​ time?

b. What is the probability that in the next six​ flights, two or fewer will be on​ time?

.c. What is the probability that in the next six​ flights, at least four flights will be on​ time?

d. d. What are the mean and standard deviation for this​ distribution?

Let x be a random variable that represents white blood cell count per cubic milliliter of whole blood. Assume that x has a distribution that is approximately normal, with mean μ = 6350 and estimated standard deviation σ = 2750. A test result of x < 3500 is an indication of leukopenia. This indicates bone marrow depression that may be the result of a viral infection.

(a) What is the probability that, on a single test, x is less than 3500? (Round your answer to four decimal places.)


(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x?

The probability distribution of x is approximately normal with μ_x = 6350 and σ_x = 2750.

The probability distribution of x is approximately normal with μ_x = 6350 and σ_x = 1375.00.    

The probability distribution of x is not normal.

The probability distribution of x is approximately normal with μ_x = 6350 and σ_x = 1944.54.

What is the probability of x < 3500? (Round your answer to four decimal places.)


(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)


(d) Compare your answers to parts (a), (b), and (c). How did the probabilities change as n increased?

The probabilities decreased as n increased.

The probabilities stayed the same as n increased.    

The probabilities increased as n increased.

If a person had x < 3500 based on three tests, what conclusion would you draw as a doctor or a nurse?

It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.    

It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

BIO 260 SP20 Assignment #6 One Sample t-tests. INSTRUCTIONS Provide responses on the Assignment 6 Answer Sheet

1. A new drug that is meant to increase hematocrit in humans and that may be a cheaper alternative to EPOGEN is being tested. A clinical trial was performed in which fifteen volunteers took the drug and had their hematocrit measured. The known mean hematocrit in humans is 45%.

Data:

37.8 46.8 42.8 38.3 42.7 47.3 49 39.9 43.6 45.7 52.9 43.6 47.4 47.3 43.4

A. What is the “population” we are estimating the parameters for with our sample? B. State the null and alternative hypothesis.
C. Report the sample statistics on the answer form
D. Calculate the t- score for the sample vs the "reference"

E. Determine the t- critical value for an alpha of 0.05 from a t-table and record.
G. Write out your statistical conclusion, i.e. do you reject, or fail to reject the null, and at what p-value?

H. Write out your biological conclusion, i.e. is the mean hematocrit of the sample significantly larger, smaller, or no different?

BIO 260 SP20 Assignment #6 One Sample t-tests. INSTRUCTIONS Provide responses on the Assignment 6 Answer Sheet

2. Consider a population of lizards living on an island. We believe that they may be members of a species called Tribolonotus gracilis. The mean length of Tribolonotus gracilis is known to be 8cm. The following length values (cm) were obtained for a sample of individuals from the island:

11.3 11.5 9.2 11 6.9 8.9 6.9 11.3

Do these lizards have sizes that are consistent with their being Tribolonotus gracilis or not?

(Base your decision on the observed vs. expected mean length.)

A. Use the correct syntax for null and alternative hypothesis. B. record tcalc, tcrit and ?.
C. State your Statistical Conclusion
D. State your Biological Conclusion

E. include p-value.

G. use the phrase "significantly smaller", "significantly larger" or "not significantly different"

1. What is the difference between a test of independent means and a test of matched means?

2. How would I calculate a test of matched means? what is the“matched” means?

3. Do you think both these tests ( a test of independent means and a test of matched means) are reasonable? Fair? Why or why not? Common concerns might be assumptions of the test being met, the practicality of the test, etc.

A poll reported that only 1283 out of a total of 1964 adults in a particular region said they had a​ "great deal of​ confidence" or​ "quite a lot of​ confidence" in the military. Assume the conditions for using the CLT are met. Complete parts​ (a) through​ c below.

A. Find a 95​% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the​ military, and interpret this interval.Answer (____, ____) (3 decimal places)

Interpret this interval. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Type integers or decimals rounded to three decimal places as​ needed.)

We are 95% confident that the population proportion of adults having a great deal or quite a lot of confidence in the military is between Answer ____ and _____

b. Find an 80% confidence interval. Interpret it.

The 80% confidence interval for the proportion that express a great deal of confidence or quite a lot of confidence in the military is Answer ____ and _____(Round to 3 decimal places as​ needed.)

Interpret this interval. Select the correct choice below and fill in the answer boxes to complete your choice. ​(Type integers or decimals rounded to three decimal places as​ needed.)

We are 80​% confident that the population proportion of adults having a great deal or quite a lot of confidence in the military is between Answer _____ and _____

c. Which interval is​ wider? The width of the 95% confidence interval is 0.058and the width of the 80% confidence interval is Answer _____The 99% interval is wider. ​(Round to three decimal places as​ needed.)

a) A k-out-of-n system is one that will function if and only if at least k of the n individual components in the system function. If individual components function independently of one another, each with probability 0.8, what is the probability that a 4-out-of-6 system functions?

b) Obtain ?(?(?−2)) where ? ~???????(?)

c) Service calls arrive at a maintenance center according to a Poisson process, with average 3.1 calls per minute.

(i) Obtain the probability that no more than 4 calls arrive in a minute.

(ii) Obtain the probability that more than 7 calls arrive in a three-minute interval

1. Describe the two components of a one variable regression equation.

2. Explain what a residual is when developing a regression model.

Q1. Historically, all matches in a tennis tournament used to have an average duration of
85.5 minutes and a standard deviation of 10.5 minutes. A researcher anticipates that these
have changed now. A sample of 36 match duration times are selected. The mean duration
time for selected matches is 89.5 minutes and standard deviation of duration of selected
matches is 8 minutes. Consider the following questions. [1+4+2+1+4+2 = 14 points]
(a) Suppose the researcher wants to test, at 5% level, the claim that the recent matches in
that tournament has different durations, on an average, compared to the past.
(i) Write it as ToH problem by describing ?! and ?" using mathematical notation for the
parameter of interest in the context of the problem.
(ii) Determine CR and conclude appropriately.
(iii) Now, solve the same problem by finding the p-value and show that you reach the same
conclusion as in Part (ii)

A multi-disciplinary team in the US formulates a hypothesis that links intimate partner violence (IPV) during pregnancy and damage to the fetal brain. They define the outcome of interest as the presence of abnormal findings including blood clot in the fetal brain detected by ultrasound during pregnancy. All infants included in the study later undergo neurological examination after birth to confirm prenatal (before birth) ultrasound observations. To determine whether a woman was actually a victim of intimate partner violence, the investigators used a questionnaire. Respondents were initially asked whether they had ever experienced any violence from their spouse. Based on more detailed questions the violence experienced was categorized into the following subtypes:

1. Physical violence included instances of pushing/shoving, throwing objects, slapping, twisting arm, punch, hitting with an object, kicking, dragging, attempting to strangle or burn, threatening with a weapon, attacking with a weapon;
2. Emotional violence included verbal or physical public humiliation, verbal threat to the woman or her family;
3. Sexual violence referred to being forced to have sex or being forced to perform sexual acts.

The questionnaire was originally validated and found to capture 4 of every 5 cases of true IPV in a random sample comprising 500 pregnant women.

The US investigators proceeded with their longitudinal study and enrolled 300 pregnant women among whom 30% screened positive on ultrasound. Of the total 150 pregnant women with negative history of IPV, 30 had abnormal fetal brain ultrasound findings. Using odds ratio, calculate the association between IPV during pregnancy and intra-uterine fetal brain damage.

1. Using odds ratio, calculate the association between IPV during pregnancy (as assessed by questionnaire) and intra-uterine fetal brain damage (as assessed by ultrasound)
2. Is IPV during pregnancy associated with fetal brain damage?
3. Explain your response for question 2.
4. Based on the information provided, construct the true 2-by-2 table, working backwards from the misclassified table (misclassification of IPV). (You are given information regarding the sensitivity of the questionnaire. Since you are not given any information on specificity, assume it is 100%)

5.Now with your new true 2-by-2 table without misclassification of IPV, calculate the association between IPV during pregnancy and intra-uterine fetal brain damage (use the OR as your measure of association)

6. Now with your new true 2 by 2 table without misclassification of IPV, is IPV during pregnancy associated with fetal brain damage?

      7. What is the effect of disease misclassification on the odds ratio?

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1488 and a standard deviation of 292. The local college includes a minimum score of 2014 in its admission requirements. What percentage of students from this school earn scores that fail to satisfy the admission requirement? P(X < 2014) =________ % Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

A study was conducted on students from a particular high school over the last 8 years. The following information was found regarding standardized tests used for college admitance. Scores on the SAT test are normally distributed with a mean of 1011 and a standard deviation of 198. Scores on the ACT test are normally distributed with a mean of 21.5 and a standard deviation of 3.8. It is assumed that the two tests measure the same aptitude, but use different scales.

If a student gets an SAT score that is the 49-percentile, find the actual SAT score.
SAT score =
Round answer to a whole number.

What would be the equivalent ACT score for this student?
ACT score =
Round answer to 1 decimal place.

If a student gets an SAT score of 1367, find the equivalent ACT score.
ACT score =
Round answer to 1 decimal place.

The physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. The distribution of the number of daily requests is bell-shaped and has a mean of 46 and a standard deviation of 7. Using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 46 and 67?


ans = __________%