# 6.4.q7 - Student Grady Simonton Instructor Shawn Pan-ini...

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Unformatted text preview: Student: Grady Simonton Instructor: Shawn Pan-ini Date: 3.-"'18..-"'10 Colu'se: 1\-Iat11119: Elementary Statistics - Spring 2010 - C‘RN: 49239 - 16 weeks Book: Triola: Elementary Statistics. Me Time: 4:12 PM A genetics experiment involves a population of fruit ﬂies consisting of 2 males named Boone and Carlton and 2 females named Donna and Edith. Assume that two fruit ﬂies are randomly selected with replacement. a. After listing the possible samples and ﬁnding the proportion of males in each sample, use a table to describe the sampling distribution of the proportion of males. To list the possible samples ofsize n = 2 taken with replacement from the population Boone, Carlton, Donna, Edith, let's select the names in alphabetic order. For example, the ﬁrst sample would be Boone-Boone, or B-B. Similarly, the next sample would be B-C. Continuing with the process above, we ﬁnd the possible samples shown below. B-B; B-C; B-D; B-E; C-B; C-C; C-D; C-E; D-B; D-C; D-D; D-E; E-B; E-C; E-D; E-E Now ﬁnd the proportion of males in each sample. Sample Proportion of males Sample B-B l C-B B-C l C-C B-D 0.5 C-D B-E 0.5 C-E Sample Proportion of males Sample W E-B D—C 0.5 E-C D-D 0 E-D D-E 0 E-E Proportion of males 1 l 0.5 0.5 Proportion of males 0.5 0.5 0 0 To describe the sampling distribution of the proportion of males, condense the sample table by listing the distinct proportions with their corresponding probabilities. The distinct proportions are 0, 0.5, and 1. To ﬁnd the corresponding probability for each proportion, divide the number of occurrences of that proportion by the total number of samples. Proportion of males Probability 0 4;“ 16 0.5 8;“ 16 l 4 f 16 b. Find the mean of the sampling distribution. To do so, use the equation 11 = Z [x - P(x)], where x is each distinct proportion and P00 is the corresponding probability. Page 1 Student: Grady Sinlonton Colu'se: 1\-Iat11119: Elenlentaiy Statistics - Spring 3010 - C‘RN: 49339 Instructor: Shawn Pan-'ini - 16 weeks Date: 3.-"'18.-"'10 Book: T1‘iola: Elenlentaiy Statistics. Me Time: 4:13 PM 2b: - P00] (0-4r16)+(0.5-8r16)+(1-4r16) 0.5 1; II C. Is the mean of the sampling distribution [from part (b)] equal to the population proportion of males? lfso, does the mean of the sampling distribution ofproportions always equal the population proportion? Calculate the population proportion of males. The population proportion of males in the population is 0.5. Therefore, the mean of the sampling distribution, 0.5, is equal to the mean of the given population, 0.5. To determine if this is always the ease, remember that proportion is an unbiased estimator. Thus, the mean of the sampling distribution ofproportions is always equal to the population proportion because proportion is an unbiased estimator, meaning that sample proportions tend to target the population proportion. Page 3 ...
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