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# Sampling Theory STA 144

UCD

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This 2 page Class Notes was uploaded by Carmen Mayer on Tuesday September 8, 2015. The Class Notes belongs to STA 144 at University of California - Davis taught by Staff in Fall. Since its upload, it has received 265 views. For similar materials see /class/191915/sta-144-university-of-california-davis in Statistics at University of California - Davis.

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Date Created: 09/08/15

h A l What is the sampling distribution of 1 851 For the population in Example 21 nd the sampling distribution of SI for a b an SRS of size 3 without replacement an SRS of size 3 with replacement For each draw the histogram of the sampling distribution of y Which sampling distribution has the smaller variance and why One way of selecting an SRS is to assign a number to every unit in the population then use a random number table to select units from the list A page from a random number table is given in Appendix E Explain why each of the following methods will or will not result in an SRS a The population has 742 units and we want to take an SRS of size 30 Divide the random list into segments of size 3 and throw out any sequences of three digits not between 001 and 742 If a number occurs that has already been included in the sample ignore it If we used this method with the rst line of random numbers in Appendix E the sequence of threedigit numbers would be 749 700 699 611 136 We would include units 700 699 611 and 136 in the sample For the situation in part a when a random threedigit number is larger than 742 eliminate only the rst digit and start the sequence with the next digit With this procedure the rst ve numbers would be 497 006 611 136 and 264 The population has 170 items Using the procedures described in part a or b we would throw away many of the numbers from the list To avoid this waste divide every random three digit number by 170 and use the rounded remainder as the unit in the sample If the remainder is 0 use unit 170 As in parts a and b eliminate the duplicates For the sequence in the rst row of the random number table the numbers generated would be 69 20 19 101 136 The population has 200 items Take twodigit sequences of random numbers and put a decimal point in front of each to obtain the sequence 74 97 00 69 96 Then multiply each decimal by 200 to get the units for the sample convert 00 to 200 148 194 200 138 192 A school has 20 homeroom classes each homeroom class contains between 20 and 40 students To select a student for the sample draw a random number between 1 and 20 then select a student at random from the chosen class Do not include duplicates in your sample For the situation described in pait e select a random number between 1 and 20 to choose a class Then select a second random number between 1 and 40 If the number corresponds to a student in the class then select that student if the second random number is larger than the class size then ignore this pair of random numbers and stait again As usual eliminate duplicates from your list pediatric outpatient clinic They found i unassisted walking among the children Age months 1 9 10 11 Number of children 13 35 44 a Construct a histogram of the distribut distributed Do you think the samplir normally distributed Why or why n 1 Find the mean standard error and a walking 6 Suppose the researchers want to do 2 a 95 CI for the mean age of onset o the estimated standard deviation for t to take One quantity that is often of interest for t that are overdue for a vaccination Some that percentage in a large practice thou g consuming Cullen 1994 took a sample family practice to estimate the proportio a What sample size in an SRS without the proportion with 95 con dence 1 Cullen actually took an SRSWR 01 for vaccination Give a 95 CI for vaccination Requires probability In the population in the population are missing the value SRS of size 300 would have no missing At one university there were 807 facul College of Liberal Arts and Science in publications for 1992 1993 were availat member the number of refereed publicati available on the database so the inves separately A frequency table for numbei of 50 faculty members Refereed publications I 0 Faculty members i 28 a Plot the data using a histogram Des b Estimate the mean number of publice error for your estimate 9 12 Why or why not d Estimate the proportion of faculty members with no publications and give a 95 CI for your estimate De ne a con dence interval procedure by CIS 3 196 SEOS is 196 81305 Using the method illustrated in Example 27 nd the exact con dence level for a con dence intervalbased on an SRS without replacement of size 4 from the population in Example 21 Does your confidence level equal 95 A letter in the December 1995 issue of Dell Champion Jan39er Puzzles stated I ve noticed over the last several issues there have been no winners from the South in your contests You always say that winners are picked at random so does this mean you re getting fewer entries from the South In response the editors took a random sample of 1000 entries from the last few contests and found that 175 of those came from the South 3 Find a 95 CI for the percentage of entries that come from the South b According to Statistical Abstractof the United States 309 of the US population live in states that the editors considered to be in the South Is there evidence from your con dence interval that the percentage of entries from the South differs from the percentage of persons living in the South The data set agsrsdat also contains information on other variables For each of the following quantities plot the data and estimate the population mean for that variable along with its stande error Give a 95 CI for your estimate a Number of acres devoted to farms in 1987 b Number of farms 1992 c Number of farms with 1000 acres or more 1992 11 Number of farms with 9 acres or fewer 1992 The Special Census of Maricopa County Arizona gave 1995 populations for the following cities City Population Buckeye 4857 Gilbert 59338 Gila Bend 1724 Phoenix 1149417 Tempe 153821 Suppose you want to estimate the percentage of persons who have been immunized against polio in each city and can take an SRS of persons What should be your sample size in each of the ve cities if you want the estimate from each city to have margin of error of 4 percentage points For which Cities does the nite population correction make a difference 13 Histogram of the means of 100U san pies 0 Example 24 200 150 100 fuequency 50 0 240000 2800 00 320000 Estimated Sampling Distribution Decision theoretic approach for sump decision theory approach two functior L01 2 loss or C12 2 cost ofl Suppose for some constants c0 c1 and L01 2 kVG C n C0 What sample size n minimizes the tote Requires computing If you have a l tribution of 515 by repeatedly taking sa of sample values A histogram of the replacement from the data in Example be slightly skewed but still appears a 100 from this population be suf cient 500 samples with replacement of size draw a histogram of the 500 means T1 as the bootstrap see Efron and Tibshi Section 93 The Internet site wwwgolfc0ursecor variety of information about each com the course and facilities Data from a golfsrsdat on the data disk 3 Display the data in a histogram for How would you describe the shap b Find the average weekday green standard error for your estimate 1 rou 21779 J UUO 16472 1131 93725 71132 58118 22432 22113 56189 20126 71728 86130 91732 72912 27134 08650 56117 50647

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