- DQ 1 Consider the following news headline, "Cigarette Smokers Make Lower College Grades Than Nonsmokers." The article goes on to say that researchers at a university collected information on the rate of cigarette smoking (total number of cigarettes smoked in a one-month period) and the college student's current GPA for completed college courses. They found that those with higher levels of cigarette use had lower GPAs, and vice versa. What can you rightfully conclude from this? Why? Be specific about what this kind of information may indicate and mean.DQ 2A pharmaceutical company conducts a study to evaluate the relationship between length of time taking drug X and size of tumor. They enlist 2,400 patients with the same type of benign tumor who have been on drug X for varying lengths of time (measured in days). They find that the longer the patient is on the drug, the smaller the patient’s tumor size (measured in volume). In fact, they report the results as r(2398) = -.21, with significance of p < .0001. What is your initial perception of this information? What are other ways, beyond looking at the p-value alone, you could use to try to interpret what this outcome of r(2398) = -.21 tells us about the relationship between length of time taking drug X and the size of the tumor? Support your responses.

Answer questions #1-3. Show Work. 1. A basketball player makes a shot 72.1% of the time (0.721 as a decimal). Study the player’s next three shots by doing the following: a. Draw a tree diagram and label all of the probabilities on the tree. b. Find and label the probability for each branch of the tree diagram. c. Build a probability model showing the probability of the player making 0, 1, 2, or 3 shots. 2. A bucket contains 4 red balls and 5 orange balls. Two balls are pulled from the bucket, one after another, without replacement. Build a tree diagram showing the different possible outcomes for the two marbles being drawn. Be sure each branch is labeled with its individual probability and include the probability at the end of each branch. 3. Consider that 45% of Americans own a dog, 25% of Americans own a cat, and 40% of Americans own neither. Draw a Venn Diagram for this situation. Be sure to label every region of the Venn Diagram with a word AND the percentage of Americans that fall in each category.

The approach to hypothesis testing that's presented in Ch. 8 is the "standard" approach. As such, it's the most widely used and you have to understand it. But there's another approach to testing hypotheses that is more intuitive, and in this assignment we'll explore it.(1) For this assignment you need access to a spreadsheet program (preferably Excel) or a plain text editor. You also need to be able to take screenshots on your computer. If you need help to do that, go to take-a-screenshot.org.(2) Download Ch08 Homework.docx and tips.txt.(3) Review Example 8.1 (p. 247-253). We're told that the average tip from male customers to waitresses is 16 percent with a standard deviation (SD) of 3 percent (p. 247). For this example, we're supposed to consider these to be the mean and SD of the population we're interested in. For a sample of 36 male customers, the mean tip was 17.2 percent (p. 252).When testing hypotheses, the question is usually a simple one. When we calculate the mean of a sample, we know it will not be exactly equal to the mean of the population the sample came from. But what we want to know is whether the difference between the sample mean and the population mean is merely due to chance or if it's so large that it probably didn't occur just by chance alone. In other words, is it so large that there's probably something else going on that accounts for the large difference?The resampling approach to answering this question starts with the fact that we have to try to answer this question using only one sample. It would be easier to answer the question if we could replicate (repeat) this study by drawing A LOT MORE samples from the same population so we could see if the single sample we've got is typical or unusual. If we had many more samples to compare, we could see if a sample with a mean of 17.2 has a low probability or a high probability of occurring.Using computer power, we actually can draw a lot more samples from the population. The data set called tips.txt was created to simulate the population from which these researchers drew their sample. It contains 20,000 values which represent tips given by male customers to waitresses. It was created so that its mean and SD closely match the mean and SD of the original population. The mean and standard deviation of this simulated population are not exactly 16 and 3, but they're extremely close.(4) Now go to www.rossmanchance.com/ISIapplets.html and click on One Mean in the Quantitative Response category at the top of the page. (You may have to inactivate popup blockers for this site in order for the applet to appear.) On the left is a data box. If there's anything in it, click Clear to empty the box.(5) We will load this box with our simulated population data. There are two ways to do this. If you're using Excel, open tips.txt. Then click the capital A at the top of the first column. This will select the entire contents of the column. Once it's selected, save the contents of column A to your clipboard. If you're using a plain text editor, open tips.txt, select the contents, and save to your clipboard.(6) Back on the applets site, click inside the data box and paste the contents of tips.txt from your clipboard.(7) Click Use Data below the box. If you've done everything correctly you'll see two columns. The first is the ID column identifying each of the 20,000 customers. The second column consists of the customers' tips (as a percentage).Just below Use Data you should see Population size: 20000. Below that you should see a histogram of the population data. You should also see that the population mean is extremely close to 16 and the population standard deviation is extremely close to 3.(8) Click in the little box next to Show Sampling Options.(9) For Number of samples enter 1000. This tells the applet to draw 1,000 random samples from the population. These 1,000 samples are the LOT MORE samples referred to above. Comparing the original researchers' mean of 17.2 to the means of these 1,000 additional samples will allow us to see how typical or unusual a sample mean of 17.2 is.(10) For Sample size enter 36. This tells the applet that the size of each of these 1,000 samples should be n = 36, which matches the sample size used by the original researchers.(11) Click Draw Samples to actually create the 1,000 new samples. What appears in the box are the values of the most recent sample, that is, sample #1,000. If you scroll through these values you'll see there's 36 of them. The blue dots in the population histogram at the lower left show you where, in the population, the 36 values in this sample came from. It should be pretty obvious that they were drawn at random. The Most Recent Sample graph is a dotplot (similar to a histogram) of the 36 values in this most recent sample. We should expect the mean of this sample (or any of the 1,000 samples we've drawn) to be close to the population mean since the population is approximately normal and since our sample size is greater than 30.The histogram at the bottom right shows the distribution consisting of the means of the 1,000 samples.(12) In the original study, the mean of the sample was 17.2 (percent). So enter 17.2 in the empty box next to Count Samples Greater than ≥ and click Count. This tells the applet to show the fraction of the 1,000 sample means that were as large as 17.2 or larger. We also see this result as the probability of a sample mean as large as 17.2 or larger. If this probability is smaller than .05 (the alpha level used for this hypothesis test), it tells us that a sample mean this large has an extremely low probability of occurring when the population mean is 16. The vertical red line also shows where, in the distribution of sample means, this sample of 17.2 falls.(13) Take a screenshot of the applet page to be submitted as part of this assignment.(14) Use the information from the applet to answer the questions on Ch08 Homework.docx, and then save it.Summing up what we've doneIn the original experiment reported in Example 8.1, the average tip (regardless of the color of the waitress's shirt) was 16%. But when waitresses wore red shirts, a sample of 36 customers tipped an average of 17.2%. The question was whether the sample mean of 17.2% was so much larger than the population mean of 16% that it was very unlikely to have happened by chance. If it was unlikely to have happened by chance, this would suggest that something else besides pure chance caused tips to be larger when waitresses wore red. The researchers' hypothesis was that wearing red made the waitresses appear more attractive to the male customers, causing them to give larger tips.To test that hypothesis, we simulated replicating the original experiment 1,000 times. We reasoned that if an average tip as large as 17.2% could happen fairly often just by chance, then we could reject the researcher's hypothesis that wearing red caused tips to increase. And instead, we would accept the null hypothesis that wearing red had no effect on tipping.