Question

The proportion of left-handed people in the general population is about 0.10. To simulate this population, we constructed a collection in which p = 0.10. We then conducted four simulations, drawing random samples of different sizes from this collection. Here you see the resulting sampling distributions and corresponding summary tables: Measures from Sample of Collection 1 Measures from Sample of Colection 1 N=200 0.100095 proportion_lefthanded 0.0221608 1005 S1 = mean) S2 = stdDev> S3 = count) Measures from Sample of Colection 1 000 0 0 0.10 0.30 0.15 0.20 0.25 proportion Jefthanded Measures from Sangle of Collection 1 N=100 0.100557 proportion_lefthanded 0.0287191 1005 S1 - mean( S2 = stdDev> S3 = count> Measures from Sample of Collection 1 0.00 0.05 0.10 0.30 0.15 020 0.25 proportion_lefthanded Measures from Sample of Collection 1 N=50 0.102706 proportion_lefthanded 0.0418382 1005 S1 = mean() S2 = stdDev> S3 = count) Measures from Sample of Collection 1 0.00 005 010 0.30 0.15 020 025 proportion lefthanded Meatures from Sample of Collection 1 N=20 0.100896 proportion_lefthanded 0.067461 1005 S1 = mean> S2 = stdDev> 53 count() 0.00 005 0.10 0.30 015 020 025 proportion lefthanded

Answer 1

a) Given 200 so a 1 Left handed people poutre proportion Samples A:0:10 :: A) ;) fou N: 200 Here the sample size length a considered as portion of the totot proportion in considered, hence this shifts the average of the sample hence we get mean = 0.100095 g the standard deviation is the total count Samples is 1005 As shown in the simulation graph, the density of Samples is increased around the mean. 0.0.22 1608 il: 1005 0) For N = 100 Here the sample length reduced to coo Whereas count remains same AS riduced sample size : the samples in the simulation graph are apart by a small distance meaning the density when compared to N: 200 ore The mean here increases as formple frequency Idensity in reduced .. Same in the with standard deviation, here as mean is increased so deviation funsin the complete proportion ako increases.. S: 0 :0.28 7191 mean: 0.100 S52. care N 100 case. Became iii) for N= so For this care the sample size is further reduced further reduced making it lightly dense when compared to both the mean & standard deviation both increase further when compared to previous care. standard deviation of the mean: 0:10 2706 0.04.18382

mean, M Mw.so > MN.100 >M: 200 count 1005 for standard deviation >o > N.SO N: 100 N.200