When bonding​ teeth, orthodontists must maintain a dry field. A new bonding adhesive has been developed to eliminate the necessity of a dry field.​ However, there is concern that the new bonding adhesive is not as strong as the current​ standard, a composite adhesive. Tests on a sample of 9 extracted teeth bonded with the new adhesive resulted in a mean breaking strength​(after 24​ hours) of overbar x=5.78 Mpa and a standard deviation of s=0.41 Mpa. Orthodontists want to know if the true mean breaking strength is less than 6.35 ​Mpa, the mean breaking strength of the composite adhesive.

A) We must assume that the sample was not random and selected from a population with a highly skewed distribution.

B.)We must assume that the sample was random and selected from a population with a distribution that is approximately normal.

C.)We must assume that the sample was not random and selected from a normally distributed population.

D).We must assume that the sample was random and selected from a population that is highly skewed.

a.) The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 30%. If 14 calculators are selected at random, what is the probability that more than 6 of the calculators will be defective?

b.) An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.70 that troubles in a residential service can be repaired on the same day. For the first six troubles reported on a given day, what is the probability that: Fewer than 3 troubles will be repaired on the same day?

c.) Given the length an athlete throws a hammer is a normal random variable with mean 60 feet and standard deviation 2.5 feet, what is the probability he throws it between 55 feet and 65 feet?

d.) If x is a binomial random variable where n = 100 and p = 0.30, find the probability that x is more than 25 using the normal approximation to the binomial. Check the condition for continuity correction.

In a recent national survey, 30 Canadian adults aged 18-24 reported having used cannabis for the first time since its legalisation in 2018 compared to 68 among the 25-44-year-olds. Out of the 1500 survey respondents, 125 were 18-24-year-olds and 400 were in the 25-44 age group. The Public Health Agency has been concerned that the first time use of cannabis among the younger cohort is higher than that among the older cohort.

a) Formulate the appropriate statistical hypotheses to test if the proportion of first-time cannabis users is higher among younger adults.  

b) Perform the appropriate hypothesis test manually using the P-value approach and a 2% significance level. Make sure you verify that the relevant assumptions and conditions are met for the test.  

c) Using the corresponding confidence level, calculate a one-sided confidence interval for the difference in the proportions of first-time cannabis users among the two age groups.  

d) Are the results from b) and c) above consistent and why?

e) Use Minitab or other appropriate software to perform the calculations in b) and c) and comment on any differences.

Question 3: EatWell Inc., a large fast-food chain company of Canada, wants to test two versions of a new product before launching its full production. They select a random sample of individuals among their regular clients and ask them to participate in an experiment to rate the product according to an assessment grid worth 20 points. The 15 individuals who accepted to participate had to come to a specific company location on two occasions during a given week to test the two versions of the product. It was a randomized experiment in which the version assigned to participants during their first visit was selected at random and participants did not know which version they were rating. Scores data of each participant are included in the Minitab file EatWell_Scores.mtw and in the Excel file Assign2.xlsx under the EatWell_Scores tab.

a) Examine and comment on the distribution of the ratings for the two versions of the product and decide which statistical test is the most appropriate for this type of data. Justify your selection based on the assumptions and conditions required for the most appropriate test selected.  

b) Regardless of your answer in a) above, perform a relevant parametric test using a 10% significance level to determine if there is a difference between the two versions of the product. Make sure you show your Minitab or other software output along with an interpretation of the results (manual calculations are not required here).  

c) Now, perform a Wilcoxon signed rank test to verify if there is a significant difference at the 10% level between the two versions of the product based on these ratings. Show your manual calculations including the T+ and T- statistics and conclude based on the critical value approach.  

d) Use Minitab or other software to perform the test in c) above and comment on the computed Pvalue and your conclusion in c).  

e) Compare your results from the parametric and non-parametric tests above and state what the final conclusion regarding the two versions of the product should be.

here is the data from EatWell_Scores.mtw

A college offers teaching in Math, English, Chemistry, and Biology. The number of students enrolled in each subject is listed below. If the college can only afford to hire 19 teachers, determine how many teachers should be assigned to each subject using Jefferson's method.

(a)

(b) What modified divisor did you use?

Question 2: The Office of the Superintendent of Bankruptcy of Canada (OSBC) is developing a new index to measure the vulnerability of firms in the new technology industry. The index is a ratio of current assets to current liabilities adjusted for various factors specific to this industry. The OSBC wants to compare the index among healthy and failed firms for validation purposes. They expect that failed firms should have a lower index than the healthy ones. Based on a Canadian business registry, they draw a random sample of 68 firms still in operations and another random sample of 33 firms which failed in the last 3 years. Index data for the sampled firms based on their latest financial statements are included in the Minitab file Bankruptcy_Index.mtw and in the Excel file Assign2.xlsx under the Bankruptcy_Index tab. Data is below:

a) Use Minitab or other appropriate software to produce boxplots of the index values for the two groups of firms and comment on their distribution. 2  

b) Use an appropriate statistical test to determine, at the 1% significance level, whether the data provide evidence of a higher average index for the healthy firms. Make sure you provide your manual calculations using the critical value approach.  

c) Calculate manually a 99% one-sided confidence interval for the difference in the average index of healthy and failed firms and compare your results with b) above.

d) Use Minitab or other appropriate software to perform the calculations in b) and c) above and comment on any differences

Here is the data for Bankruptcy_Index.mtw

Each time a fisherman casts his line, a fish is caught with probability p, independent of whether a fish is caught on any other cast of the line. The fisherman will fish all day until a fish is caught and then he will quit and go home. Let Ci denote the event that on cast i the fisherman catches a fish. Draw the tree for this experiment and find P[C1], P[C2], and P[Cn] as functions of p.

DO NOT POST SOMEONE ELSE'S ANSWER. PLEASE SHOW FULL, COMPLETE ANSWER. THANK YOU!

Please Answer All 4 questions

The British Museum, located in the Bloomsbury area of London in the United Kingdom, is a public institution dedicated to human history, art, and culture. To ensure the safety of its famous and precious collections, engineers selected the 100 most crowded and popular exhibition areas within the museum and checked their environment to avoid potential damages to collections.

1.) b) What is the sample in this problem?
The British Museum
All exhibition areas in the British Museum which are open to the public.
The 100 most crowded and popular exhibition areas.
The environment in the British Museum.

Pepsi is a carbonated soft drink manufactured by PepsiCo. Coca-Cola, or Coke, is a carbonated soft drink manufactured by The Coca-Cola Company. These two drinks are popular all over the world. They share quite similar color and taste thus it is hard to say which one is better than the other. Forty people are randomly selected to determine which one is better. Each person is blind-folded and asked to drink a small cup of Pepsi and the same amount of Coke. Since they are blind-folded, they don’t know which drink they are drinking. Then they are asked to select which drink they prefer.

c.) What is the factor or treatment in this study?
40 cups of Pepsi and Coke
The drink people prefer
Type of drinks
All people around the world
All drinks
40 participants

(0.5 pts.) d) What is the outcome variable of this study?
All drinks
Type of drinks
The drink people prefer
40 participants
All people around the world
40 cups of Pepsi and Coke

(1 pt.) e) State a possible source of bias in this study. Feel free to speculate beyond the explicit statement of the question. However, nothing that is assumed can be contradicted by what is stated. Please include any assumptions that you are making.

Find a research article that used an ANOVA and a post-hoc analysis in their methods/results. Describe how the ANOVA and post-hoc analysis was used to answer the research. List what did it compare, where the group differences were found in the post-hoc and share the levels of the dependent and independent variable(s). Provide article.

PLEASE ANSWER ALL 4 QUESTIONS

The owner of a bar wants to know whether their customers prefer Johnnie Walker Whiskey or Seagram's Whiskey. The bar owner is undecided over which of two possible experiments she should use. In Experiment 1, each customer rates only one of the two drinks. In Experiment 2, each customer evaluates both types of whiskey.

Experiment 1
Flip a coin for each customer to choose which type of drink (s)he will taste. Then each person rates the drink from 1 to 10.

Experiment 2
Flip a coin for each customer to choose which types (s)he will taste first. After trying both types of drinks, ask which of the two varieties that (s)he prefers.

Which of the two given designs should the bar owner choose? Please explain your answer.

(2 points) Please indicate which type of sampling design is most appropriate for each of the following studies. The choices are SRS, stratified random sampling, and matched pair design.

Does air pollution induce DNA mutations in mice? 20 male mice were housed in a polluted industrial area downwind from a steel mill. An addition 20 male mice were housed in an unpolluted rural location 30 kilometers away.

Does smoking affect class performance? 300 14 to 22 year old smokers and 300 14 to 22 year old nonsmokers were contacted and asked about their gpa's.

A researcher wants to know the effect of climate change on the percent yield of the corn harvest. They collected the data for the same 50 plots in both 2016 and 2017 for their study.

Question 3: (Minitab or Excel – Excel is easiest)

The table below shows the average distance of each of the nine planets from the sun, and the length of the year (in earth years). Note that Pluto is not considered a planet anymore (check it out on Wikipedia).

a) Plot the Length of the Year (the response) versus the Distance from the Sun (the explanatory variable). Describe the scatterplot.

b) Fit a linear model that will help predict the Length of Year a planet from its Distance from the Sun. Does the model provide a good fit?

c) Produce the residual plot for the model you developed in 3b. The plot shows a clear trend. Describe it. We are going to improve the model by re-expressing both distance and length of year in the logarithmic scale. This approach is indicated by the large amount of variance in both variables as well as strong positive skewness of their distributions (you can check both of these facts for yourself by making stemand-leaf plots and obtaining summary statistics—no need to include this step in your paper).

d) Take the base ten logarithm of the distance and length of year variables. We will refer to the new variable as the Log(distance) and Log(length). Follow the Minitab directions below on how to proceed.

e) Fit a regression line to predict Log(length) from Log(distance).

f) Obtain the residual plot for the model.

g) Did we improve the model?

Now you may understand why you need a statistics course. As a forensics analyst, how would you use statistical flow analysis to identify a compromised host? How about to confirm or disprove data leakage? How would it be used to create a profile of an individual? Can statistical flow analysis be used to prevent either a host becoming compromised or data being leaked?