How well materials conduct heat matters when designing houses, for example. Conductivity is measured in terms of watts of heat power transmitted per square meter of surface per degree Celsius of temperature difference on the two sides of the material. In these units, glass has conductivity about 1. The National Institution of Standards and Technology provides exact data on properties of materials. Here are 11 measurements of the heat conductivity of a particular type of glass.

1.11 1.05 1.12 1.07 1.13 1.07 1.08 1.15 1.17 1.18 1.13

(a) We can consider this an SRS of all specimens of glass of this type. Make a stemplot. (Enter your answers from smallest to largest. Enter NONE in any unused answer blanks.)

Stems Leaves

1.0 1.0 1.1 1.1

Is there any sign of major deviation from Normality?

The stemplot shows that the data are not skewed and have no outliers.

The stemplot shows that the data is skewed to the left with one outlier.

The stemplot shows that the data is skewed to the right with one outlier.

(b) Give a 80% confidence interval for the mean conductivity. (Use 3 decimal places.)

(__________ , __________)

Conditional Probability Problem: An urn contains 5 red balls, 4 green balls, and 4 yellow balls for a total of 13 balls. If 5 balls are randomly selected without replacement what is the probability of selecting at least two red balls given that at least one yellow ball is selected?

a) 0.59

b) 0.61

c) 0.63

d) 0.65

e) 0.67

Share with your classmates the data visualisations you have created based on the sample data set, by posting screenshots of your charts and graphs on the class-wide forum. Reflect on how appropriate the different visualisations are for authentic representation of the data, and express which aspects of data visualisation play an important role in “telling the truth” about your data.

How many 3-digit numbers can we make using the digits 1, 2, 3, 4, 5, 6 without repetitions? How about with repetitions (meaning different digits can hold the same number; e.g., 223 and 444 are valid 3-digit numbers in the with repetitions case)?

Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with a mean of 650 and a standard deviation of 120. Suppose you take a SRS of 35 students from this distribution. What is the probability that a SRS of 35 students will spend an average of between 600 and 700 dollars? Round to five decimal places.

I'm using 2005 NFL stats to come up with a multiple linear regression analysis models with the winning percentage being the dependent variable. My question would be, what are the most significant variables that are used in deciding an NFL team's capacity to win? Passing yards, rushing game, defense or field goals are some of my independent variables. But I’m considering adding the defensive stats to the regression. How do I complete my presentation subtopics?

Presentation:

I. Introduction: Summarize your topic and research question. Why did you choose this topic? How does your research question fit within the topic?

II. Model Selection: Justify your model type selection. Why did you choose your model type to address the research question? Use theories and research to support the justification of your selection.

III. Model Process: Justify the process used to build the model. Why did you make the specific decisions you made while building your model? Use theories and research to support the justification of your selection.

IV. Model Analysis: Analyze the model. What are its strengths and limitations? What impact do these strengths and limitations have on the applicability of your model for different purposes and situations?

V. Results Analysis: Analyze your results. What are the strengths and limitations of your results? How do the results impact the applicability of your model for different purposes and situations?

VI. Model Defense: Defend your model by responding to all questions from your instructor with coherent and relevant responses. Use relevant research support in your defense.

The Business School at State University currently has three parking lots, each containing 155 spaces. Two hundred faculty members have been assigned to each lot. On a peak day, an average of 70% of all lot 1 parking sticker holders show up, an average of 72% of all lot 2 parking sticker holders show up, and an average of 74% of all lot 3 parking sticker holders show up.

a. Given the current situation, estimate the probability that on a peak day, at least one faculty member with a sticker will be unable to find a spot. Assume that the number who show up at each lot is independent of the number who show up at the other two lots. Compare two situations: (1) each person can park only in the lot assigned to him or her, and (2) each person can park in any of the lots (pooling). (Hint: Use the RISKBINOMIAL function.) If needed, round your answer to a whole percentage and if your answer is zero, enter "0".

b. Now suppose the numbers of people who show up at the three lots are highly correlated (correlation 0.9). How are the results different from those in part a? If needed, round your answer to a whole percentage.

Do College students who have volunteered for community service work differ from those who have not? A study obtained data from 57 students who had done service work and 17 who had not. One of the response variables was a measure of attachment to friends, measured by the Inventory of Parent and Peer Attachment. Here are the results. Group Condition n x s__ 1 Service 57 105.32 14.68 2 No Service 17 96.82 14.26 a. Do these data give evidence that students who have engaged in community service and those who have not differ on average in their level of attachment to their friends?

Point estimates often need to be nested in layers of analysis, and it is the Invariance Principle that provides a pathway for doing so. An example would be estimating Mu after having to estimate Alpha and Beta for some distributions. In simpler statistics class exercises (like those we've seen up until now), this is typically avoided by providing the lower level parameters within exercises or problems (e.g. asking you for Mu by giving you the Alpha and Beta). The only real options we've had prior to this unit for estimating lower level parameters has been trial-and-error: collecting enough data to form a curve that we then use probability plots against chosen parameter values until we find a combination of parameters that "fits" the data we've collected. That approach works in the simplest cases, but fails as our problem grows larger and more complex. Even for a single distribution (e.g., Weibull) there are an infinite number of possible Alpha-Beta combinations. We can't manually test them all.

Point estimation gets us around all of that by providing the rules needed to actually calculate lower level parameters from data. We sometimes need to be able to collect a lot more data to use this approach, but it's worth it. We'll be able to calculate more than one possible value for many parameters, so it's important that we have rules for selecting from among a list of candidates.

Discuss what some of those rules are, and how they get applied in your analysis. If an engineering challenge includes "more than one reasonable estimator," (Devore, p. 249, Example 6.1 in Section 6.1) how do engineers know which to pick, and what issues arise statistically and in engineering management when making those choices?

Prevalence is used for?

t is election time and voters are going to the polls to cast their vote for their favorite candidates. A researcher was interested to study whether there is a significant difference in patterns of voting turnout among three regions: Eastern, Western and Central. She randomly selected 12 voting precincts from each region and calculated the sum of squares of the rate of participation as follows: SSB= 3,342.89 SSW= 7,265.42 Write the ANOVA formula and conduct an ANOVA test of patterns for voting turnout. Write the hypotheses HO and H1, calculate F ratio and interpret the results.

A high school physics teacher wondered if his students in the senior class this year will be more likely to go into STEM (Science, Technology, Engineering, Mathematics) majors than Social Science and Liberal Arts majors. He asked each of his 65 students about their first choice for major on their college applications and conducted a Chi-square test for goodness of fit with an alpha level of .05 to see if the number of students choosing each category differs significantly.

35 – STEM

20 – Social Sciences

10 – Liberal Arts

a. What is the variable in this test? What type of variable is it (nominal, ordinal, or continuous)? (1 point total: .5 for each question)

b. State the null and alternative hypotheses in words (1 point total: .5 for each hypothesis)

c. Calculate X² statistic (2 points total: 1 for final answer, 1 for the process of calculating it)

d. Calculate the degree of freedom and then identify the critical value (1 point total: .5 for df, .5 for critical value)

e. Compare the X² statistic with the critical value, then report the hypothesis test result, using “reject” or “fail to reject” the null hypothesis in the answer (1 point total, .5 for each answer)

f. Explain the conclusion in a sentence or two, to answer the research question. (1 point)

A machine produces pipes used in airplanes. The average length of the pipe is 16 inches. The acceptable variance for the length is 0.3 inches. A sample of 17 pipes was taken. The average length in the sample was 15.95 inches with a variance of 0.4 inches.

A workshop makes tables. The cutting and sanding operations are independent. Based on historical data, under normal conditions, 1% of cut wood for the tables, and 2% of sanded wood for the tables are defective. Assume that one table is randomly selected from a lot of cut and sanded tables. a. What is the probability that at least one of the operations (cutting and sanding) will be defective? b. What is the probability that in a production lot of 10 tables, none of the tables is defective? c. What is the expected number of defective tables in a production lot of 15 tables? What is the standard deviation?