GRINNELL MAT 209 - Lab 9: Rectangularity

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Lab 9: RectangularityLab 9: Rectangularity*adapted from Garfield, delMas, and Chance’s work found at http://www.gen.umn.edu/research/stat_tools/Label the rectangles in the population from 00 to 99. (Call Rectangle 1, 01; call Rectangle 2, 02; and so on up toRectangle 99, which you should call 99. Call Rectangle 100, 00). Each person in your group estimate the average (µ) rectangle size (area) for the population of 100 rectangles.name_____________________Estimate_____ name_____________________Estimate_____name_____________________Estimate_____ name_____________________Estimate_____Use row 130 from your random number table to select two different simple random samples one of size 5 and one with n = 25 from the population (sample with replacement -- so that it is possible to select the same rectangle more than once). For each sample, list the labels of the rectangles selected, list the areas, and then calculate the value of.X (the average area of each of your samples) Random Sample 1 Random Sample2Label Area Label Area x = x =1. For each sample size n = 5 and 25 construct an 80% Confidence interval for the mean area of the rectangles (µ) in the population {assume  = 5.69 }2. For each sample size n = 5 and 25 construct an 95% Confidence interval for µ {assume  = 5.69 }13. We know that µ = 6.26 (by calculating the average size of all 100 rectangles). Let’s assume you repeated the sampling process on page one 1000 times, calculating a total of 2000 .X and 4000 confident intervals.(a) What percent of the 80% confidence intervals would you expect to include the value of6.26?m= (b) What percent of the 95% confidence intervals would you expect to include the value of6.26?m= (c) Explain how increasing the confidence level from 80% to 95% changed the confidence intervals.(d) Explain how increasing the sample size changed the confidence interval. 4. (a) How close where your original estimates to 6.26? How close were your .X’s to 6.26?(b)Explain why using the sample mean based on a sample size of 5n  may not be a good idea to construct our confidence intervals or testing hypothesis. (c) Explain why it is absolutely necessary to use a table of random digits or some type of random number generator to select our samples.The p-value is the probability, computed under the assumption that0H is true, of obtaining a test statistic value at least as favorable toAH as the value that actually resulted from the data. If the p-value is small enough,0H is rejected. Rejecting the null hypothesis, when in fact it is true, is called a Type I error. The significance level, ,a is the chance of committing a Type I error. If the p-valuea�,0H is rejected. If the p-valuea>,0H is not rejected. 5. Test0: 6.26H m= versus: 6.26.AH m� at 5% level of significance( .05).a = Use .Xbased on n= 25z = p-value = Do you reject or fail to reject HoSince in this problem0H is true, a correct decision would be to fail to reject0.H An incorrect decision would be to reject0.H (This would be a Type I error.) If we repeated this hypothesis test 1000 times based on 1000 SRS, How often would you expect to get an .Xthat caused a Type I error?26. Write the number of the description in the right column next to the symbol in the left column that it describes. The Symbol: Refers to: ____ a) /n1) variability of observations in a sample____ b) x 2) variability of sample means in a sampling distribution____ c)  3) variability of all observation in a population____ d) s 4) center of all observations in a population____ e)  5) center of all observations in a sample 7 . A sample of 50 data measurements is selected from a population of temperatures. A sample mean of 20  is obtained. What would be your best estimate of , the population mean?__a. It would be exactly 20 __b. It would be close to 20 __c. I wouldn’t be able to make an estimate. I know nothing about . It’s an unknown parameter andthis is just one sample.__d. Other________________________8. If you take a sample of data from the population described in #73 above, what information will you be able to calculate from these data? Check as many as apply:__a.  __b. s__c. __d.x 9. Circle the symbols below which represent parameters. Underline the symbols that represent sample statistics. s x 10. For the symbols listed below, circle the ones which vary from sample to sample? s x 11. For the symbols listed below, circle the ones which do not vary from sample to sample? s x 12. Two different samples will be taken from a same population of test scores where the population mean and standard deviation are unknown. The first sample will have 25 data values (n = 25), and the second sample will have 64 data values (n = 64). A 95% confidence interval will be constructed for each sample to estimate the population mean. Which confidence interval would you expect to have greater precision in estimating the population mean?a. I expect both confidence intervals to have the same precision.b. I expect the confidence interval based on the sample of 64 data values to be more precise.c. I expect the confidence interval based on the sample of 25 data values to be more precise.3d. I can’t determine which will have more precision.13. Imagine that there are 100 different researchers each studying the sleeping habits of college freshmen. Each researcher takes a random sample of size 50 (n = 50) from the same population of freshmen. Each researcher is trying to estimate the mean hours of sleep that freshmen get at night, and each one constructs a 95% confidence interval for the mean. Approximately how many of these 100 confidence intervals will NOT capture the true mean?a. None d. about halfb. 1 or 2 e. 95 to 100c. 3 to 7 f. other 14. Which of the following values will ALWAYS be within the 95% confidence interval limits?a. The population mean ()b. The sample mean (x)c. The sample size (n)d. The standard deviation of the sample (s)15. Two researchers are going take a sample of data from the same population of physics students. Researcher A will select a random sample of students from among all students taking physics. Researcher B’s sample will consist only of the students in her class. Both researchers will construct a 95% confidence interval for the mean score on the physics final exam using their own sample data. Which researcher’s method has a 95% chance of capturing


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GRINNELL MAT 209 - Lab 9: Rectangularity

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