Quarter 4 Stats Project!!!
5.2 Designing Experiments Q: In the mid 1900s, a common treatment for angina was called internal mammary ligation. In this procedure doctors made small incisions in the chest and tied knots in two arteries to try to increase blood flow to the heart. It was a popular procedure - 90% of patients reported that it helped reduce the pain. In 1960, Seattle cardiologist Dr. Leonard Cobb carried oat an experiment where he compared ligation with a procedure in which he made incisions but did not tie off the arteries. The sham operation proved just as successful, and ligation procedure was abandoned as a treatment for angina. A) What is the response variable in Dr. Cobb's experiment? B) Dr. Cobb showed that the sham operation was just as successful as ligation. What term do we use to describe the phenomenon that many subjects report good results from a pretend treatment? C) The ligation procedure is an example of the lack of an important property of a well designed experiment. What is the property?
A: A) Treatment for Angina B) Placebo Effect C) Control Group
6.1 Simulation Q:State how you would use the following aids to establish a correspondence in a simulation that involves a 75% chance: A) A coin B) A six-sided die C) A random digit table (table B) D) A standard deck of playing cards
A: A) You would have to flip the coin twice after assigning the one success combination and three failure combinations. B) Assign one success and three failures, than remove two numbers on the die. Last step would roll the die. C) You would go through the numbers, and numbers 00-74 would be a success, and numbers 75-99 would be a failure. D) You would make one suit a success and the other three a failure.
1.2 Describing Distributions with Numbers 1.4 3.4 9.1 1.6 10.5 2.5 0.9 4.1 5.9 17.1 6.8 1.8 0.3 0.9 0.8 2.0 1.1 1.6 2.6 0.4 0.6 1.8 4.8 1.1 3.0 1.1 1.1 2.0 6.0 7.1 3.6 8.1 3.6 1.8 0.4 1.1 1.2 5.5 1.0 Q: Given the numbers above make a stemplot, and describe it's distribution. (Remember the 5 main things we look for when describing the distribution and the new way with IQR to find the new spread)? What's the five number summary?
A: Key: 0|3= 0.3 0|3446899 1|011111246688 2|0056 3|0466 4|18 5|59 6|08 8|1 10|5 17|1 Shape: skewed to the right center:1.8 spread: 0.3-17.1 Gaps:10.6- 17 There is one outlier, 17
1.1 Displaying Distributions with Graphs 28 32 25 34 38 26 25 18 30 26 28 13 20 21 17 16 21 23 14 32 25 21 22 20 18 26 16 30 30 20 50 25 26 28 31 38 32 21 Q: Given the numbers above make a stemplot, and describe it's distribution. (Remember there are 5 main things we look for when describing the distribution) Are there any outliers?
A: Key: 1|3= 13 0| 1|3466788 2|0001111235556666888 3|0001222488 4| 5|0 Shape: symmetrical center:25 spread: 13-50 Gaps:39-49 There is one outlier, 50.
3.1 Scatterplots and Correlation Q:How would you describe the direction, form, and strength of the relationship from the scatterplot?
-positive -linear -moderate
Quarter 4 Project by Mike Wong, Briona Moss, and Chelsea Suratos
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3.2 Least Squares Regression Q: Some data were collected on the weight of a male white laboratory rat following its birth. A scatterplot of the weight (in grams) and time since birth (in weeks) shows a fairly strong positive linear relationship. The linear regression equation weight=100+40(time) models the data fairly well. (a) Interpret the slope of the regression line in this setting. (b) Interpret the y intercept of the regression line in this setting.
(a) For every extra week of age, a rat will increase its weight by an average of 40 grams. (b) The estimated weight of this rat at birth is 100 grams.
3.3 Correlation and Regression Wisdom Q: "Empathy" means being able to understand what others feel. To see how the brain expresses empathy, researchers recruited 16 couples in their mid-twenties who were married or had been dating for two years. They zapped the man's hand with an electrode while the woman watched, and measured the activity in several parts of the woman's brain that would respond to her own pain. Brain activity was recorded as a fraction of the activity observed when the woman herself was zapped with the electrode. The women also completed a psychological test that measures empathy. Will women who are higher in empathy respond strongly when their partner has painful experience? Here are data for one brain region: (see answer side) (a) Analyze these data in a way that will help answer the researchers' question. Follow the Data Analysis Toolbox. (b) Is Subject 16 influential for the correlation? Justify your answer. (c) Is Subject 16 influential for the least squares line? Justify your answer.
(a) The data varies, although certain numbers show that as the level of empathy increased, so the did the brain activity. (b) Yes, Subject 16 is influential for the correlation because its result causes an incline and it has an effect on the rest of the data. (c) No, Subject 16 is not influential for the least squares regression line because the data will not appear as linear and will be scattered.
5.1 Designing Samples Q: A campus newspaper plans a major article on spring break destinations. The authors intend to call a few randomly chosen resorts at each destination to ask about their attitudes toward groups of students as guests. Here are the resorts listed in one city. The first step is to label the members of this population as shown. ________________________________________________ 01 Aloha Kai | 02 Anchor Down | 03 Banana Bay | 04 Banyan Tree | 05 Beach Castle | 06 Best Western | 07 Cabana | 08 Captiva | 09 Casa del Mar | 10 Coconuts | 11 Diplomat | 12 Holiday Inn | 13 Lime Tree | 14 Outrigger | 15 Palm Tree | 16 Radisson | 17 Ramada | 18 Sandpiper | 19 Sea Castle | 20 Sea Club | 21 Sea Grape | 22 Sea Shell | 23 Silver Beach | 24 Sunset Beach | 25 Tradewinds | 26 Tropical Breeze | 27 Tropical Shores | 28 Vernanda ________________________________________________ Enter Table B at this line 131, and choose three resorts
A: Line 131: 05007 16632 81194 14873 04197 85576 45195 96565 The way you answer this question is once the subjects are numbered you look through the line and looking at every two digits. In this case the first three (3) double digit numbers comes up they are the chosen numbers. The chosen numbers also has to be between 01 and 28. The answer for this questions are: 05 - Beach Castle 19 - Sea Castle 04 - Banyan Tree
4.1 Transforming to Achieve Linearity Q: If you have taken a chemistry class, then you are probably familiar with Boyle's law: for gas in a confined space kept at a constant temperature, pressure times volume is a constant (in symbols, PV= k). Students collected the following data on pressure and volume using a syringe and a pressure probe. (a) Make a scatterplot suitable for predicting pressure from volume. Describe the direction, form, and strength of the relationship. Are there any outliers? (b) If the true relationship between the pressure and volume of the gas is PV= k, we can divide both sides of this equation by V to obtain P=k/V, or P= k(1/V). So if we graph pressure against the reciprocal of volume, we should see a linear relationship. Perform this transformation of the volume data, and graph P versus 1/V. Did this information achieve linearity? (c) Find the least-squares regression equation for the transformed data. How well does this model fit the transformed data? Justify your answer using a residual plot and r^2. (d) Let's try a different transformation of the data. Take the reciprocal of the pressure values (1/P), and plot these against the original volume measurements. Find the least-squares regression equation. Why did this transformation achieve linearity? (e) Use your models in part (c) and (d) to predict the pressure in the syringe when the volume of gas is 15 cubic centimeters. How similar are the predictions?
A: (a) The relationship is strong, negative, and curved, with no outliers. (b) Yes, the information achieves linearity. (c) P^ =0.3677 + 15.8994(1/V). r^2 = 0.9958 indicates almost a perfect fit. The residual plot shows a definite patters, which should be of some concern, but the model still provides a good fit. (d) Let y=1/P; the least-squares regression line is y^=0.1002 + 0.0398V. r^2= 0.9997, and the residual plot shows a random scatter. This transformation achieves linearity because V=k/P (e) The Model in part (c): 1.4277 atmospheres; model in part (d): 1.4343 atmospheres. They are the same to the nearest one-hundredth of an atmosphere.
4.2 Relationships between Categorical Variables Q: Here are data on the numbers of degrees earned in 2005-2006, as projected by the National Center for Education Statistics. The table entries are counts of degrees in thousands. Describe briefly how the participation of women changes with the level of degree.
A: It can be seen that as the level of degree advances, there seems to be a decline in participation of women, with an exception of Bachelor's degree.
2.1 Measures of Relative Standing and Density Curves Q: A normal density curve has which of the following properties? (a) It is symmetric. (b) It has a peak centered above its mean. (c) The spread of the curve is proportional to it standard deviation. (d) All of the properties (a) to (c) are correct. (e) None of the properties (a) to (c) is correct.
A: The answer is (d) all of the properties (a) to (c) are correct. It should look like this
6.2 Probability Models Q: Probability is a measure of how likely an event is to occur. Match each statement about an event with one of the probabilities that follow. (The probability is usually a much more exact measure of likelihood than is the verbal statement.) 0, 0.01, 0.3, 0.6, 0.99, 1 A) This event is impossible. It can never occur. B) This event is certain. It will occur on every trial of the random phenomenon. C) This event is very unlikely, but it will occur once in a while in a long sequence of trials. D) This event will occur more often than not.
A: The general way to answer this question is to read the question, interpret what it is asking, and match the correct percent to the simulation set up by the problem. A) 0.0 B) 1.0 C) 0.3 D) 0.6
6.3 General Probability Models Q: At a self-service gas station, 40% of the customers pump regular gas, 35% pump midgrade, and 25% pump premium gas. Of those who pump regular, 30% pay at least $20. Of those who pump midgrade, 50% pay at least $20. And of those who pump premium, 60% pay at least $20. What is the probability that the next customer pays at least $20?
A: The recommended way to solve this problem, is to take it step by step and draw it out the tree way. The way to solve this specific problem is that it is basically asking what is the percent of the percent in a certain category. For regular it would have to be 30% of 40%, midgrade would be 50% of 35%, and premium would be 60% of the 25%. To find a percent of a percent they would have to multiple each other. Once multiplied all three gas types, add up the ending decimals. That total will be the percent of people who would be paying at least $20. The answer is about .445 people will be buying at least $20 worth of gas.
4.3 Establishing Causation Q:A serious study once found that people with two cars live longer than people who own only one car. Owning three cars is even better, and so on. There is a substantial positive correlation between number of cars X and length of life Y. What lurking variables might explain the association between number of cars owned and life span?
A:The lurking variable for this question is the amount of money that the person has. The more cars the person has the more money the person has, which means that they could get better health care, or better food to live longer.