Explor 1

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Apr 3, 2024

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E XPLORATION 1.5: Eye Dominance pg. 1 Exploration 1.5: Eye Dominance Name(s): Angie Ashby Just like handedness where people prefer to use one hand over another, eye dominance, sometimes called eyedness, is the tendency to prefer to see using one eye over the other. Interestingly, the side of the dominant eye does not always match that of the dominant hand. Let’s investigate whether people are equally likely to have left-eye or right-eye dominance by collecting some data from you and your classmates. 1. To figure out which of your eyes is the dominant eye, carry out the following “dominant eye test”: • Extend both your arms in front of you and create a triangular opening using your thumbs and pointer fingers. • With both eyes open, center your triangular opening on a distant object such as a clock or projector. • Close your left eye. If the object stays centered in your triangular opening, your right eye (as that is the one that’s open) is your dominant eye. If the object is no longer in the triangular opening your left eye is your dominant eye. • Double check this by closing your right eye. If the object stays centered in your triangular opening, your left eye (as that is the one that’s open) is your dominant eye. If the object is no longer in the triangular opening, your right eye is your dominant eye. Record whether you have left-eye or right-eye dominance. right-eye Check the course schedule page to find the results from the entire class. Before we combine your data with the data from your classmates, let’s think about what we want to test here. Conventional wisdom says that more often people are right-handed than left, so for now let’s use our research hypothesis to be that more often people tend to have right-eye dominance than left-eye dominance. 2. In this study with your classmates: (a) What are the observational units in this study? [ The students whose eyes are being tested ] (b) What is the variable that is recorded? [ Left or right eye dominance ] (c) Describe the parameter of interest in words. (Use the symbol π to represent this parameter.) [ π= probability of people being more right eye dominant ] (d) If right-eye and left-eye dominance are equally prevalent, what would you expect the numerical value of the parameter to be? Is this the null hypothesis or the alternative hypothesis? [ Null = .5 ] (e) If people are more likely to be right-eye dominant that left, what can you say about the numerical value of the parameter? Is this the null hypothesis or the alternative hypothesis? [ Alternative = > .5 ]
E XPLORATION 1.5: Eye Dominance pg. 2 3. These data were collected in the Data Collection survey on the first day of class. The results are posted on the course schedule page. There were 36 total responses with 12 left-eye dominant and 24 right-eye dominant . Calculate and report the sample proportion who are right-eye dominant. [ 24/36 sample proportion = .67 ] 4. To have a larger sample size to analyze, combine your class results with the results from some of the author’s classes, in which 70 of 115 students had right-eye dominance. Now what are the sample size and the sample proportion that are right-eye dominant? Sample size: [ 94/151 ] Sample proportion: [ .62 ] 5. Use the One Proportion applet to test the hypotheses from #2d and #2e. (a) Describe the shape of the null distribution of sample proportions. Does this shape look familiar? Where is the null distribution centered? Does this make sense? Check the Summary stats box and report the mean and standard deviation as reported by the applet. Shape: [ normal, bell shaped] Familiar? [ Yes ] Center? [ 0.5 ] Why does this make sense? [ The null must be true? ] Mean: [0.501 ] SD: [ 0.041 ] (b) Approximate the p-value and summarize the strength of evidence that the sample data provide regarding the research hypothesis. [ 0.004 , there is very strong evidence against the null ] (c) Determine the standardized statistic, z , and summarize the strength of evidence. Confirm that the strength of evidence obtained using the standardized statistic is similar to that obtained using the p-value. [ (0.62 - .501) / .041= 2.9 ] Theory-based Approach (One-Proportion z -test) In #5a, you probably described the shape of the null distribution using words such as bell-shaped, symmetric, or maybe even normal. You have seen many null distributions in this chapter that have had this same basic shape. You should have also noticed that the null distributions have all been centered at the hypothesized value of the long-run proportion used in the null hypothesis. You probably could have predicted that your null distribution was going to be somewhat bell-shaped and centered at 0.50. You probably would have a harder time predicting your null distribution’s variability (standard deviation), but this too can be predicted in advance, as we will see shortly. We can use mathematical models known as normal distributions (bell-shaped curves) to approximate many of the null distributions we have generated so far in this text. When rules and theories are used to predict what the value of the standardized statistic and p-value would be if someone carried out a simulation, we call the approach a theory-based approach . The normal distribution provides a second way, in addition to simulation, to approximate a p-value.
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