Exam 8: Regression, Associations, and Predictive Modeling

Suppose that our editor was hoping that the book would have a mean word length of 6.5 letters. Does this sample indicate that the authors failed to meet this goal? Test an appropriate hypothesis and state your conclusion.

Good CDs Brian is a systems manager for a large company. In his work, he has found that about 5% of all CDs he orders are bad. He needs to give one of the executives at his company five good CDs. Conduct a simulation to estimate how many CDs Brian will have to check to get five good CDs for the executive. a. Describe how you will use a random number table to conduct this simulation. b. Show three trials by clearly labeling the random number table given below. Specify the outcome for each trial. Trial Simulation Outcome \#1 03242506921897728370 \#2 78695214028552581183 \#3 60809067653999681915 c. State your conclusion.

The vast majority of states and the District of Columbia have adopted the Common Core State Standards (CCSS) for math and English language arts. Do teachers support the CCSS? In March 2003, The American Federal of Teachers (AFT) asked AFT member teachers "Based on what you know about the Common Core State Standards and the expectations they set for children, do you approve or disapprove of your state's decision to adopt them? " The following results were reported in American Educator (Volume 32, No. 2, Summer 2013, pg. 3): 27% Strongly Approve; 48% Somewhat Approve; 14% Somewhat Disapprove; 8% Strongly Approve; 3% Not Sure. A district superintendent asked the same question to the teachers in her district to assess the level of teacher support for the CCSS within the district. She obtained the following results. Response Strongly Approve Somewhat Approve Somewhat Disapprove Strongly Disapprove Not Sure Frequency 55 106 28 32 9 a. Test an appropriate hypothesis to ascertain if the district CCSS approval distribution matches the national AFT approval distribution. b. Which response impacted your decision the most? Explain what this means in the context of the problem.

Which of these variables is most likely to follow a Normal model for U.S. adults?

State your conclusion

The relationship between the number of hours a person practices a task and the time it takes them To complete the task is calculated to have R $\mathrm { R } - \mathrm { sq } = 56.7 \%$ 56)7%. The value of the correlation coefficient is

Insulators Ceramics engineers are testing a new formulation for the material used to make insulators for power lines. They will try baking the insulators at four different temperatures, followed by either slow or rapid cooling. They want to try every combination of the baking and cooling options to see which produces insulators least likely to break during adverse weather conditions. a) What are the experimental units? b) How many factors are there? c) How many treatments are there? d) What is the response variable?

A company has tried to improve the effectiveness of its dishwashing detergent and wants to see if it Works better than the original formula. They use 6 identical new dishwashers and load them Identically with dirty dishes. Three packs of each of the two types of detergent are used, and they Are randomly assigned to one of the six dishwashers. After the load is run, they rate each load for Overall cleanliness. Which of the following is true?

In a large 2lb. bag of candies (the true fun size!) 15% of the candies are green. The chances of Pulling out at least one green candy in three tries is…

A manufacturing plant for recreational vehicles receives shipments from three different parts vendors. There has been a defect issue with some of the electrical wiring in the recreational vehicles manufactured at the plant. The plant manager wonders if all of the vendors might be contributing equally to the defect issue. The plant manager reviews three samples of quality assurance inspections from the last six months, one from each of the vendors. The data are shown in the table below. Test an appropriate hypothesis to decide if the plant manager is correct. Give statistical evidence to support your conclusion.

Interpret the confidence interval in this context.

Explain what your P-value means in this context.

Penicillin assimilation Doctors studying how the human body assimilates medication inject a patient with penicillin, and then monitor the concentration of the drug in the patient's blood for several hours. The data are shown in the table. Time elapsed (Hours) Concentration (Units/cc) 1 42 2 28 3 19 4 13 5 9 6 6 7 4 a. Straighten the scatterplot by re-expressing these data and create an appropriate model for predicting the concentration of penicillin. b. Use your model to estimate what the concentration of penicillin will be after 8 hours.

An elementary school principal wants to know the mean number of children in families whose Children attend this school. He checks all the families using the school's registration records, and we Create a 95% confidence interval based on a t-distribution. This procedure was not appropriate. Why?

M&Ms The Mars candy company starts a marketing campaign that puts a plastic game piece in each bag of M&Ms. 25% of the pieces show the letter "M", 10% show the symbol "&", and the rest just say "Try again". When you collect a set of three symbols "M", "&", and "M" you can turn them in for a free bag of candy. About how many bags will a consumer have to buy to get a free one? Use a simulation to find out. a. Explain how you will use the random numbers listed below to conduct your simulation. b. Carefully label your simulation for 2 trials. c. State your conclusion.

Create a model to predict diamond costs from the size of the diamond.

Researchers investigating the association between the size and strength of muscles measured the forearm circumference (in inches) of 20 teenage boys. Then they measured the strength of the boys' grips (in pounds). Their data are plotted. a. Write a few sentences describing the association. b. Estimate the correlation. r = ________ c. If the point in the lower right corner (at about 14" and 38 lbs.) were removed, how would the correlation become stronger, weaker, or remain about the same? d. If the point in the upper right corner (at about 15" and 75 lbs.) were removed, would the correlation become stronger, weaker, or remain about the same?

Name and describe the kind of bias that might be present if the statistics teacher decides that instead of randomly selecting students to survey on how they feel about the course she just… a. asks students to volunteer for the survey. b. gives the survey during class one day.

Which is important in designing a good experiment? I. Randomization in assigning subjects to treatments. II. Control of potentially confounding variables. III. Replication of the experiment on a sufficient number of subjects.

Grape juice and blood pressure Researchers who wanted to see if drinking grape juice could help people lower their blood pressure got 120 non-smokers to volunteer for a study. They measured each person''s blood pressure and then randomly divided the subjects into two groups. One group drank a glass of grape juice every day while the other did not. After sixty days the researchers measured everyone's blood pressure again. They reported that differences in changes in blood pressure between the groups were not statistically significant. a. Was this an experiment or an observational study? Explain briefly. b. Briefly explain what "not statistically significant" means in this context. c. Briefly explain why the researchers randomly assigned the subjects to the groups. d. Since everyone's blood pressure was measured at the beginning and at the end of the study, the researchers could have simply looked at the grape juice drinkers to see if their blood pressure changed. Briefly explain why the researchers bothered to include the control group. e. Briefly explain why the researchers studied only non-smokers. f. Other researchers now plan to replicate this study using both smokers and non-smokers. Briefly describe the design strategy you think they should use.