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MATH 331 – Homework 3 Instructor: Dr. Brown
1. Imagine the following game of chance. There are four dollar bills on the table. You roll a
fair die repeatedly. Every time you fail to get a six, one dollar bill is removed. When you
get your first six, you get to take the money that remains on the table. If the money runs
out before you get a six, you?ve lost and the game is over. Let X be the amount of your
award. Find the range and the probability mass function of X.
2. The statement
SOME DOGS ARE BROWN
has 16 letters. Choose one of the 16 letters uniformly at random. Let X denote the length
of the word containing the chosen letter. Determine the range and probability mass function of X.
3. What is the probability that a randomly chosen number between 1 and 100 is divisible by
3 given that the number has at least one digit equal to 5?
4. Suppose a family has 2 children of different ages. We assume that all combinations of boys
and girls are equally likely.
a. Formulate precisely the sample space and probability measure that describes the genders of the two children in the order in which they are born.
b. Suppose we learn that there is a girl in the family. (Precisely: we learn that there is
at least one girl.) What is the probability that the other child is a boy?
c. Suppose we see the parent with a girl, and the parents tell us that this is their youngest
child. What is the probability that the older child we have not yet seen is a boy?
5. A bag contains 3 kinds of dice: seven 4-sided dice, three 6-sided dice, and two 12-sided
dice. A die is drawn from the bag and then rolled, producing a number. For example, the
12-sided die could be chosen and rolled, producing the number 10. Assume that each die
is equally likely to be drawn from the bag.
a. What is the probability that the number 6 is rolled?
b. What is the probability that a 6-sided die was chosen, given that the number 6 was
rolled?
6. We choose one of the words in the following sentence uniformly at random and then choose
one of the letters of that word (again uniformly at random):
THE QUICK BROWN FOX JUMPED OVER THE GATE
a. Find the probability that the chosen letter is O?
b. Let X denote the length of the chosen word. Determine the probability mass function
of X.
7. Insurance company X has two types of customers. An ordinary customer has an accident
during the year with probability 1%. An accident prone customer has an accident during the
year with probability 4%. 80% of the customers are ordinary customers. Pick a randomly
chosen customer. Suppose she had an accident. What is the probability that she is an
ordinary customer?
8. Let A and B be events with these properties: 0 < Pr(B) < 1 and Pr(A|B) = Pr(A|B c ) =
1
3
a. Is it possible to calculate Pr(A) from this information? Either declare that it is not
possible, or find the value of Pr(A).
b. Are A and B independent, not independent, or is it impossible to determine?
9. We choose a number between 1 and 100 uniformly at random, we denote it by X. For
each of the following choices decide whether the two events in question are independent or
not.
a. A = {X is even}, B = {X is divisible by 5}.
b. C = {X has two digits}, D = {X is divisible by 3}.
c. E = {X is a prime}, F = {X has a digit 5}.
10. Three events A, B and C satisfy the following: A and B are independent, C is a subset
of B, C is disjoint from A, Pr(A) = 1/2, Pr(B) = 1/4 and Pr(C) = 1/10. Compute
Pr(A ∪ B ∪ C).
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You collect data to, to help estimate Annual Net Sales, in thousands, of dollars to know how much money you will be making.You collect data on 27 stores to help make your decision.x1 = Rent in Thousand per monthx2 = Amount spent on Inventory in Thousand per monthx3 = Amount spent on Advertising in Thousand per monthx4 = Sales in Thousand per monthx5= How many Competitors stores are in the AreaApproximately what percentage of the variation in Annual Net Sales is accounted for by these 5 variables in this model?See Attached Excel for Data.Starbuck Sales data.xlsxQuestion 4 options:27.62% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model. 98.24% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model. 99.11% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model. 99.25% of variation in the Annual Net Sales is accounted for by Rent, Inventory, Advertising, Sales per Month and # of Competitor store in this model. Question 5 (1 point) With Obesity on the rise, a Doctor wants to see if there is a linear relationship between the Age and Weight and estimating a person's Systolic Blood Pressure. Is there a significant linear relationship between Age and Weight and a person's Systolic Blood Pressure?If so, what is/are the significant predictor(s) for Systolic Blood Pressure?See Attached Excel for Data.BP dataQuestion 5 options:No,Age, p-value = 0.9388 > .05, No, Age is not a significant predictor for Systolic BPWeight, p-value = 0 .3092 > .05, No, Weight is not a significant predictor for Systolic BPNo,Age, p-value = 0.001303023 < .05, No, Age is not a significant predictor for Systolic BPWeight, p-value = 0.023799395 < .05, No, Weight is not a significant predictor for Systolic BPYes,Age, p-value = 0.9388 > .05, Yes, Age is a significant predictor for Systolic BPWeight, p-value = 0 .3092 > .05, Yes Weight is a significant predictor for Systolic BPYes, Age, p-value = 0.001303023 < .05, Yes, Age is a significant predictor for Systolic BPWeight, p-value = 0.023799395 < .05, Yes Weight is a significant predictor for Systolic BPQuestion 6 (1 point) You move out into the country and you notice every Spring there are more and more Deer Fawns that appear. You decide to try and predict how many Fawns there will be for the up coming Spring.You collect data to, to help estimate Fawn Count for the upcoming Spring season. You collect data on over the past 10 years.x1 = Adult Deer Countx2 = Annual Rain in Inchesx3 = Winter SeverityWhere Winter Severity Index:1 = Warm2 = Mild3 = Cold4 = Freeze5 = SevereEstimate Fawn Count when Adult Deer Count = 10, Annual Rain = 13.5 and Winter Severity = 4See Attached Excel for Data.Deer data.xlsxQuestion 6 options:53.853.062.95Question 7 (1 point) In the context of regression analysis, what is the definition of an influential point?Question 7 options:Observed data points that are far from the least squares lineObserved data points that are far from the other observed data points in the horizontal directionObserved data points that are close to the least squares lineObserved data points that are close to the other observed data points in the horizontal directionQuestion 8 (1 point) The least squares regression line for a data set is yˆ=2.3−0.1x and the standard deviation of the residuals is 0.13.Does a case with the values x = 4.1, y = 2.34 qualify as an outlier?Question 8 options:YesNoCannot be determined with the given informationQuestion 9 (1 point) The following data represent the weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling. Weight (lbs.)Rolling Distance (m.)59268443974856201035987448848924653286632713910049Can it be concluded at a 0.05 level of significance that there is a linear correlation between the two variables?Question 9 options:yesnoCannot be determinedQuestion 10 (1 point) A negative linear relationship implies that larger values of one variable will result in smaller values in the second variable.Question 10 options:TrueFalseQuestion 11 (1 point) You determine there is a strong linear relationship between two variables using a test for linear regression. Can you immediately claim that one variable is causing the second variable to act in a certain way?Question 11 options:No, the correlation would need to be a perfect linear relationship to be sure.No, you should examine the situation to identify lurking variables that may be influencing both variables.No, you must first decide if the relationship is positive or negative.Yes, a strong linear relationship implies causation between the two variables.Question 12 (1 point) Which of the following describes how the scatter plot appears? Select all that apply.Question 12 options:positivenegativeneither positive or negativeQuestion 13 (1 point) The following data represent the weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling. Weight (lbs.)Rolling Distance (m.)59268443974856201035987448848924653286632713910049 Regression StatisticsMultiple R0.956806R Square0.915477Adjusted R Square0.907025Standard Error3.483483Observations12ANOVAdfSSMSFSignificance FRegression11314.321314.32108.31131.1E-06Residual10121.346612.13466Total111435.667CoefficientsStandard Errort StatP-valueLower 95%Upper 95%Intercept-8.564724.7892-1.788340.104007-19.23572.106284Weight (lbs.)0.6116910.05877510.407271.1E-060.4807310.742651Find the standard error of estimate. Round answer to 4 decimal places.___Question 13 options:Question 14 (1 point) Body frame size is determined by a person's wrist circumference in relation to height. A researcher measures the wrist circumference and height of a random sample of individuals.Model SummarybModelRR SquareAdjusted R SquareStd. Error of the Estimate1.734a.539.5254.01409a. Predictors: (Constant), Wrist Circumferenceb. Dependent Variable: HeightANOVAaModelSum of SquaresdfMean SquareFSig.1Regression621.7931621.79338.590.000bResidual531.7263316.113Total1153.51934a. Dependent Variable: Heightb. Predictors: (Constant), Wrist CircumferenceModelUnstandardized CoefficientsStandardized CoefficientstSig.BStd. ErrorBeta1(Constant)38.1775.0897.502.000Wrist Circumference4.436.714.7346.212.000What is the value of the test statistic to see if the correlation is statistically significant?Question 14 options:0.5397.5024.4365.0896.2120.734Question 15 (1 point) What are the hypotheses for testing to see if a correlation is statistically significant?Question 15 options:H0: ρ = 0 ; H1:ρ =1H0: ρ = ±1 ; H1:ρ ≠ ±1H0: r = 0 ; H1: r ≠ 0 H0: ρ = 0 ; H1:ρ ≠ 0H0: r = ±1 ; H1: r ≠ ± 1Question 16 (1 point) A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random sample of last terms students were selected and their grades are shown below. Assume scores are normally distributed. Calculate the correlation coefficient using technology (you can copy and paste the data into Excel). Round answer to 4 decimal places. Make sure you put the 0 in front of the decimal.HW3Midterm13.159.81121.987.5398.853.72824.395.2835.439.17413.266.09220.989.72918.578.9852086.215.473.2742593.259.752.2576.443.98420.279.76221.884.25823.192.9112287.8211.454.03414.971.86918.476.70415.170.4311565.1516.877.208Answer:______Question 16 options:Question 17 (1 point) Choose the correlation coefficient that is represented in the scatterplot.Question 17 options:0.830.15-0.82Question 18 (1 point) The correlation coefficient, r, is a number between:Question 18 options:0 and ∞-10 and 10-∞ and ∞0 and 100 and 1- 1 and 1Question 19 (1 point) A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random sample of last terms students were selected and their grades are shown below. Assume scores are normally distributed.HW3Midterm13.159.81121.987.5398.853.72824.395.2835.439.17413.266.09220.989.72918.578.9852086.215.473.2742593.259.752.2576.443.98420.279.76221.884.25823.192.9112287.8211.454.03414.971.86918.476.70415.170.4311565.1516.877.208Find the y-intercept and slope for the regression equation using technology (you can copy and paste the data into Excel). Round answer to 3 decimal places.ŷ=___+___xQuestion 19 options:Blank # 1Blank # 2Question 20 (1 point) Bone mineral density and cola consumption has been recorded for a sample of patients. Let x represent the number of colas consumed per week and y the bone mineral density in grams per cubic centimeter. Assume the data is normally distributed. A regression equation for the following data is ŷ=0.8893-0.0031x. Which is the best interpretation of the slope coefficient?xy10.88320.873430.889840.885250.881660.86370.863480.864890.8552100.8546110.862Question 20 options:For every additional average weekly soda consumption, a person's bone density increases by 0.0031 grams per cubic centimeter.For every additional average weekly soda consumption, a person's bone density decreases by 0.0031 grams per cubic centimeter.For an increase of 0.8893 in the average weekly soda consumption, a person's bone density decreases by 0.0031 grams per cubic centimeter. For every additional average weekly soda consumption, a person's bone density decreases by 0.8893 grams per cubic centimeter.
unit 8. anova
Design a study you would like to explore in your future or current career that could be analyzed with ANOVA. To help desig ...
unit 8. anova
Design a study you would like to explore in your future or current career that could be analyzed with ANOVA. To help design the study, please answer the following:
What is the independent variable? What are your levels of the independent variable?
What is the dependent variable?
What do you expect to find if you ran the study? Please list this out both in statistical language (feel free to make up some numbers for the results) as well as real-world language.
What would you expect to find with post hoc analyses? Which groups might be significantly different from which other groups?
Submit your post by Wednesday. Please be sure to cite your text and any other materials used.
Walden University Week 11 Use of the Chi Squared Test Statistic Discussion Paper
For this Assignment, you will consider three different scenarios. Each of these scenarios include a research question. You ...
Walden University Week 11 Use of the Chi Squared Test Statistic Discussion Paper
For this Assignment, you will consider three different scenarios. Each of these scenarios include a research question. You will examine each scenario, choose a categorical data analysis and run a sample test. To prepare for this Assignment: Review Chapters 10 and 11 of the Frankfort-Nachmias & Leon-Guerrero course text and the media program found in this week’s Learning Resources related to bivariate categorical tests. Using the SPSS software, open the Afrobarometer dataset found in this week’s Learning Resources. Next, review the Chi Square Scenarios found in this week’s Learning Resources and consider each research scenario for this Assignment. Based on the dataset you chose and for each research scenario provided, using the SPSS software, choose a categorical data analysis and run a sample test. Once you perform your categorical data analysis, review Chapter 11 of the Wagner text to understand how to copy and paste your output into your Word document. For this Assignment: Write a 1- to 2-paragraph analysis of your categorical data results for each research scenario. If you are using the Afrobarometer Dataset, report the mean of Q1 (Age). In your analysis, display the data for the output. Based on your results, provide an explanation of what the implications of social change might be. Use proper APA format, citations, and referencing for your analysis, research question, and display of output. Learning Resources Required Readings Wagner, III, W. E. (2020). Using IBM® SPSS® statistics for research methods and social science statistics (7th ed.). Thousand Oaks, CA: Sage Publications. Chapter 7, "Cross-Tabulation and Measures of Association for Nominal and Ordinal Variables"Chapter 11, "Editing Output" (previously read in Week 2, 3, 4, 5. 6, 7, and 8) Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications. Chapter 9, “Bivariate Tables” (pp. 281-325)Chapter 10, “The Chi-Square Test and Measures of Association” (pp. 327-373) Document: Chi Square Scenarios (PDF) Use these scenarios to complete your Assignment for this week. Required Media Laureate Education (Producer). (2016a). Bivariate categorical tests [Video file]. Baltimore, MD: Author. Note: The approximate length of this media piece is 5 minutes. In this media program, Dr. Matt Jones demonstrates bivariate categorical tests using the SPSS software. Accessible player --Downloads-- Download Video w/CC Download Audio Download Transcript Optional Resources Klingenberg, B. (2016). The Chi-squared test. Retrieved from https://istats.shinyapps.io/ChiSquaredTest/ Use the following app/weblink to enter your own data and obtain an interactive visual display.
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20150323234651week 8 Assignment
What percentage of observations from a standard normal distribution are below a z-value of 2.15? Look up the normal table ...
20150323234651week 8 Assignment
What percentage of observations from a standard normal distribution are below a z-value of 2.15? Look up the normal table on the left most column for ...
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