1. In order to evaluate a spectrophotometric method for the determination of titanium, the method was applied to alloy samples containing difference certified amounts of titanium. The results (%Ti) are shown below.

Sample                        Certified Value           Mean               Standard Deviation

1                      0.496                           0.482               0.0257

2                      0.995                           1.009               0.0248

3                      1.493                           1.505               0.0287

4                      1.990                           2.002               0.0212

For each alloy, eight replicate determinations were made. For each alloy, test whether the mean value differs significantly from the certified value.

Probability question please follow the comment

how do we use general inclusion and exclusion theorem to derive 4 to 5 events?

for example 3 events are that AUB=A+B-(A intersect B), but how about 4 and 5? Please you need to show me the step rather than paste the inclusion and exclusion formula and explain

A simple random sample of size

nequals=8181

is obtained from a population with

mu equals 73μ=73

and

sigma equals 18σ=18.

​(a) Describe the sampling distribution of

x overbarx.

​(b) What is

Upper P left parenthesis x overbar greater than 75.9 right parenthesisP x>75.9​?

​(c) What is

Upper P left parenthesis x overbar less than or equals 68.8 right parenthesisP x≤68.8​?

​(d) What is

Upper P left parenthesis 71 less than x overbar less than 77.8 right parenthesisP 71<x<77.8​?

Each week coaches in a certain football league face a decision during the game. On​ fourth-down, should the team punt the ball or go for a​ first-down? To aid in the​ decision-making process, statisticians at a particular university developed a regression model for predicting the number of points scored​ (y) by a team that has a​ first-down with a given number of yards​ (x) from the opposing goal line. One of the models fit to data collected on five league teams from a recent season was the simple linear regression​ model, E(y)=β0+β1x. The regression yielded the following​results: y=4.12−0.59x​, r squared equals 0.24.Complete parts a and b below.a.

Give a practical interpretation of the coefficient of​ determination, r2.

Choose the correct answer below.

A.Sample variations in the numbers of yards to the opposing goal line explain 24% of the sample variation in the numbers of points scored using the least squares line. This answer is correct.

B.There is a positive linear relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.24 is positive.

C.There is little or no relationship between numbers of yards to the opposing goal line and numbers of points scored because 0.24 is near to zero.

D.Sample variations in the numbers of yards to the opposing goal line explain 76​%of the sample variation in the numbers of points scored using the least squares line.b. Compute the value of the coefficient of​ correlation, r, from the value of r2.

Is the value of r positive or​ negative? Why? Select the correct choice below and fill in the answer box within your choice. ​(Round to three decimal places as​ needed.)

A.The coefficient of​ correlation, r=________,is positive because the estimator of beta 1β1 is positive.

B.The coefficient of​ correlation,r=__________, is positive because the estimator of beta 1β1is negative.

C.The coefficient of​ correlation,r=___________,is negative because the estimator of beta 1β1is negative.

D.The coefficient of​ correlation,r=_________,is negative because the estimator of beta 1β1 is positive.

1. Calculate the covariance between profits and market capitalization and what does the covariance indicate about the relationship between profits and market capitalization? (positive or negative).

Identify the level of measurement of each of the following variables (Nominal, Ordinal, or Scale (Ratio):

1.  County names in a state

2. Number of participants in food stamp programs.

3. Reputations of colleagues ranked on the scale of Very High to Very Low.

4. Leadership ability measured on a scale from 0 to 5.

5. Divisions within a state agency.

6. Inventory broken down into three categories: tightly controlled, moderately controlled, or minimally controlled.

About 40% of all US adults will try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 128 insurance claims to be processed int the next few days. What is the probability that -

half or more claims have been padded?

fewer than 45 of the claims have been padded:

From 40 to 64 of the claims have been padded?

More than 80 of the claims have not been padded?

The consumer food database contains five variables: Annual Food Spending per Household, Annual Household Income, Non-Mortgage Household Debt, Geographic Region of the U.S. of the Household, and Household Location. There are 200 entries for each variable in this database representing 200 different households from various regions and locations in the United States. Annual Food Spending per Household, Annual Household Income, and Non-Mortgage Household Debt are all given in dollars. The variable Region tells in which one of four regions the household resides. In this variable, the Northeast is coded as 1, the Midwest is coded 2, the South is coded as 3, and the West is coded as 4. The variable Location is coded as 1 if the household is in a metropolitan area and 2 if the household is outside a metro area. The data in this database were randomly derived and developed based on actual national norms.The consumer food database contains five variables: Annual Food Spending per Household, Annual Household Income, Non-Mortgage Household Debt, Geographic Region of the U.S. of the Household, and Household Location. There are 200 entries for each variable in this database representing 200 different households from various regions and locations in the United States. Annual Food Spending per Household, Annual Household Income, and Non-Mortgage Household Debt are all given in dollars. The variable Region tells in which one of four regions the household resides. In this variable, the Northeast is coded as 1, the Midwest is coded 2, the South is coded as 3, and the West is coded as 4. The variable Location is coded as 1 if the household is in a metropolitan area and 2 if the household is outside a metro area. The data in this database were randomly derived and developed based on actual national norms.

Provide a 1,600-word detailed, statistical report including the following:

• Explain the context of the case
• Provide a research foundation for the topic
• Present graphs
• Explain outliers
• Prepare calculations
• Conduct hypotheses tests
• Discuss inferences you have made from the results

This assignment is broken down into four parts:

• Part 1 - Preliminary Analysis
• Part 2 - Examination of Descriptive Statistics
• Part 3 - Examination of Inferential Statistics
• Part 4 - Conclusion/Recommendations

Part 1 - Preliminary Analysis (3-4 paragraphs)

Generally, as a statistics consultant, you will be given a problem and data. At times, you may have to gather additional data. For this assignment, assume all the data is already gathered for you.

State the objective:

• What are the questions you are trying to address?

Describe the population in the study clearly and in sufficient detail:

• What is the sample?

Discuss the types of data and variables:

• Are the data quantitative or qualitative?
• What are levels of measurement for the data?

Part 2 - Descriptive Statistics (3-4 paragraphs)

Examine the given data.

Present the descriptive statistics (mean, median, mode, range, standard deviation, variance, CV, and five-number summary).

Identify any outliers in the data.

Present any graphs or charts you think are appropriate for the data.

Note: Ideally, we want to assess the conditions of normality too. However, for the purpose of this exercise, assume data is drawn from normal populations.

Part 3 - Inferential Statistics (2-3 paragraphs)

Use the Part 3: Inferential Statistics document.

• Create (formulate) hypotheses
• Run formal hypothesis tests
• Make decisions. Your decisions should be stated in non-technical terms.

Hint: A final conclusion saying "reject the null hypothesis" by itself without explanation is basically worthless to those who hired you. Similarly, stating the conclusion is false or rejected is not sufficient.

Part 4 - Conclusion and Recommendations (1-2 paragraphs)

Include the following:

• What are your conclusions?
• What do you infer from the statistical analysis?
• State the interpretations in non-technical terms. What information might lead to a different conclusion?
• Are there any variables missing?
• What additional information would be valuable to help draw a more certain conclusion?

A group of high-school parents in Tucson, Arizona, in conjunction with faculty from the University of Arizona, claim that young women in the Tucson high schools not only are called on less frequently, but receive less time to interact with the instructor than do young men. They would like to see the school district hire a coordinator, spend money (and time) on faculty workshops, and offer young women classes on assertiveness and academic communication.

To make things simple, assume that instructor interactions with young men average 95 seconds, with standard deviation 35 seconds. (Treat this as population information.)

The null hypothesis will be that the average interaction time for young women will also be 95 seconds, as opposed to the alternate hypothesis that it is less, and will be tested at the 2.5% level of significance.

1. Give interpretations in context of Type I and Type II error in this situation. (Your discussion should not focus on “Null” and “Alternate”.)
2. What are the social, economic, and other consequences of (separately) Type I and Type II error?
3. Find the rejection region for this test. That is, what interaction time bounds the lower 2.5% of the distribution?
4. Assume the true mean interaction time for young women is 90 seconds. Find the power of the test.
5. Repeat part 4 for a true mean interaction time of 80 seconds.
6. What do the results in parts (4) and (5) mean in terms of your previous answers?

Indicate whether each statement represents a conceptual definition, part of an operational definition, or a hypothesis.

1. The organizational capacity of nonprofit organizations consists of their relevance, responsiveness, effectiveness, and resilience.

2. To determine the quality of police services, we asked respondents if they thought there was less, about the same, or more crime in their neighborhoods compared to the rest of the city.

3. The more politically engaged the respondents, the higher the probability that they will have a favorable attitude toward government services.

4. Home health care has been identified as an array of therapeutic and preventive services provided to patients in their homes or in foster homes.

5. Controlled items are those that must be identified, accounted for, secured, segregated, and handled in a special manner.

6. Uncontrolled items are likely to have a higher rate of wastage than controlled items.

1.

Given the following contingency table, conduct a test for independence at the 1% significance level. (You may find it useful to reference the appropriate table: chi-square table or F table)

Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

2.

A market researcher for an automobile company suspects differences in preferred color between male and female buyers. Advertisements targeted to different groups should take such differences into account if they exist. The researcher examines the most recent sales information of a particular car that comes in three colors. (You may find it useful to reference the appropriate table: chi-square table or F table)

Calculate the value of the test statistic. (Round the intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

3.

Consider the following sample data with mean and standard deviation of 20.1 and 7.3, respectively. (You may find it useful to reference the appropriate table: chi-square table or F table)

Calculate the value of the test statistic. (Round the z value to 2 decimal places, all other intermediate values to at least 4 decimal places and final answer to 3 decimal places.)

The average number of cavities that thirty-year-old Americans have had in their lifetimes is 5. Do twenty-year-olds have more cavities? The data show the results of a survey of 13 twenty-year-olds who were asked how many cavities they have had. Assume that the distribution of the population is normal.

4, 7, 4, 6, 5, 4, 5, 5, 5, 5, 5, 4, 4

What can be concluded at the αα = 0.01 level of significance?

1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:

H0:H0:  ? μ p  ? = ≠ < >       

H1:H1:  ? p μ  ? = ≠ < >    

3. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? ≤ >  αα
6. Based on this, we should Select an answer fail to reject reject accept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean number of cavities for twenty-year-olds is not significantly more than 5 at αα = 0.01, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is more than 5.
   • The data suggest the population mean is not significantly more than 5 at αα = 0.01, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is equal to 5.
   • The data suggest the populaton mean is significantly more than 5 at αα = 0.01, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is more than 5.
8. Interpret the p-value in the context of the study.
   • There is a 72.5686636% chance of a Type I error.
   • If the population mean number of cavities for twenty-year-olds is 5 and if you survey another 13 twenty-year-olds then there would be a 72.5686636% chance that the population mean number of cavities for twenty-year-olds would be greater than 5.
   • If the population mean number of cavities for twenty-year-olds is 5 and if you survey another 13 twenty-year-olds then there would be a 72.5686636% chance that the sample mean for these 13 twenty-year-olds would be greater than 4.85.
   • There is a 72.5686636% chance that the population mean number of cavities for twenty-year-olds is greater than 5.
9. Interpret the level of significance in the context of the study.
   • If the population mean number of cavities for twenty-year-olds is more than 5 and if you survey another 13 twenty-year-olds, then there would be a 1% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is equal to 5.
   • If the population mean number of cavities for twenty-year-olds is 5 and if you survey another 13 twenty-year-olds, then there would be a 1% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is more than 5.
   • There is a 1% chance that flossing will take care of the problem, so this study is not necessary.
   • There is a 1% chance that the population mean number of cavities for twenty-year-olds is more than 5.

Debate if “failing to reject the null” is the same as “accepting the null.” Support your position with examples of acceptance or rejection of the null.

Generate a simulated data set with 100 observations based on the following model. Each data point is a vector Z= (X, Y) where X describes the age of a machine New, FiveYearsOld, and TenYearsOld and Y describes whether the quality of output from the machine Normal or Abnormal. The probabilities of a machine being in the three states are

P(X = New) = 1/4

P(X = FiveYearsOld) = 1/3

P(X = TenYearsOld) = 5/12

The probabilities of Normal output conditioned are machine age are

P(Y = Normal | X= New) = 8/10

P(Y = Normal | X= FiveYearsOld) = 8/10

P(Y = Normal | X= TenYearsOld) = 4/10

Your data should consist of two vectors Y and Z both of which are of class character. Convert these to factors using the as.factor function. Analyze your simulated data using the chisq.test function with inputs x=x, y=y. Perform the analysis with the exact same function, but with simulated p-values using the inputs x=x, y=y, simulate.p.values=TRUE, B=10000. Would you trust the p-values from the asymptotic distribution or the simulated p-values more? What conclusions can you draw about your simulated data from this analysis?

An educational psychologist has developed a mediation technique to reduce anxiety. The psychologist selected a sample of high anxiety students that are asked to do the mediation at two therapy sessions a week apart. The participants' anxiety is measured the week before the first session and at each subsequent session. Below are the anxiety scores for the participants. What can the psychologist conclude with α= 0.05?

Make an interpretation based on the results.

At least one of the sessions differ on anxiety.None of the sessions differ on anxiety.    

e) Conduct Tukey's Post Hoc Test for the following comparisons:
2 vs. 3: difference =  ; significant:  ---Select--- Yes No
1 vs. 2: difference =  ; significant:  ---Select--- Yes No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 3: test statistic =  ; significant:  ---Select--- Yes No
2 vs. 3: test statistic =  ; significant:  ---Select--- Yes No