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Camera for Cataract. The following problem is modified from Rosner (2010).
A camera has been developed to detect the presence of cataract more accurately. Using this camera, the gray level of each point (or pixel) in the lens of a human eye can be characterized into 256 graduations, where a gray level of 1 represents black and a gray level of 256 represents white. To test the camera, photographs were taken of 12 randomly selected normal eyes and 9 randomly selected cataractous eyes (the two groups consist of different people). The median gray level of each eye was computed over the 10,000+ pixels in the lens. The data are given below
Under normality assumption we want to test if there is a significant difference in the gray levels between cataractous and normal eyes.
(a) Can you find any statistical evidence showing that the two gray levels are significantly different? Write down the hypotheses, conduct the test and report the p-value.
(b) Pretend that a new study is to be conducted for which the sample size is needed. From previous experiments you adopt = 16 for both groups. What sample size is needed to detect the difference of 10 in a 0:05-level testing against the two sided alternative with power 1 = 90%.
When the non-parametric statistics utilized? Write down an example.
If we fit the least-squares line to the 12 data points (one for each month) we obtain the following results from a software package. Notice that temperature is taken as the explanatory variable and crawling age as the response.
Consider the single Linear Regression Model: without an intercept (β is a scalar constant; X is a scalar random variable).
Suppose we have the following information from a simple regression: What is the coefficient of determination? What is the correlation coefficient?
A real estate agent has 2 tours. The first tour through N1and has 10 homes for sale, whereas the second tour through N2and has 5 homes for sale.
What are the 3 measures of dispersion/variation in a dataset? How do you calculate each of these 3 measures?
You have been asked to study the effects of an employee-wide training program, in a company of 500 employees, designed to reduce the amount of customer complaints.
Utilizing the .05 level, do the results support the psychologists' theory. Elucidate your answer to somebody whom has never had a course in statistics.
Give a brief definition and an example of the following: a. Descriptive Statistics b. Inferential Statistics
About 95% are between 500 +- 200; i.e. between 300 and 700 Where is the data located? Where is the "middle" of the data? How variable are the data? How spread out about the "middle" are the data?
How large a sample should be tested in order to be 99% confident that the true proportion of inedible fish is estimated to within 7%? Use 2.575 as the critical value for a 99% confidence interval.
A market research company surveyed consumers to determine their ranked preferences of energy drinks among the brands Monster, Red Bull, and Rockstar.
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