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Again, without performing any calculations, what would be less likely to occur: Obtaining a sample proportion of 0.60 or larger when randomly selecting a sample of size n = 25, or obtaining a sample proportion of 0.60 or larger when randomly selecting a sample of size n = 50? Please

Again, without performing any calculations, what would be less likely to occur: Obtaining a sample proportion of 0.60 or larger when randomly selecting a sample of size n = 25, or obtaining a sample proportion of 0.60 or larger when randomly selecting a sample of size n = 50? Please

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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We hope you noticed several important things while working through this activity. First, no matter what the sample size was, our sampling distributions were always centered at the claimed population proportion of 0.50. As the sample size got bigger, there was less variability among our sample statistics. Further, all of the sampling distributions in this case had a shape that we would consider to be approximately Normal. When the sample size is large enough (and we'll say more about what "large enough" is in a future lecture), the sampling distribution will have a Normal shape. Let's look again at our distributions of sample proportions for the three different sample sizes, from left to right below (n = 25, n = 50, and n = 100). Please answer the following questions based on what you see in the graphs below. n = 25 Mean = 0.50 n= 50 Mean = 0.50 n = 100 Mean = 0.50 Standard deviation = 0.1 Standard deviation: 0.071 Standard deviation = 0.05 0.12 0.24 0.36 0.48 0.60 0.72 0.84 0.96 0.30 0.36 0.42 0.48 0.54 0.60 0.66 0.72 0.160.24 0.32 0.400.48 0.560.64 0.720.800.88 Proportion of orange Proportion of orange Proportion of orange 2000 4000 6000 8001 00081 00071 0009 0009 12000 18000
Transcribed Image Text:We hope you noticed several important things while working through this activity. First, no matter what the sample size was, our sampling distributions were always centered at the claimed population proportion of 0.50. As the sample size got bigger, there was less variability among our sample statistics. Further, all of the sampling distributions in this case had a shape that we would consider to be approximately Normal. When the sample size is large enough (and we'll say more about what "large enough" is in a future lecture), the sampling distribution will have a Normal shape. Let's look again at our distributions of sample proportions for the three different sample sizes, from left to right below (n = 25, n = 50, and n = 100). Please answer the following questions based on what you see in the graphs below. n = 25 Mean = 0.50 n= 50 Mean = 0.50 n = 100 Mean = 0.50 Standard deviation = 0.1 Standard deviation: 0.071 Standard deviation = 0.05 0.12 0.24 0.36 0.48 0.60 0.72 0.84 0.96 0.30 0.36 0.42 0.48 0.54 0.60 0.66 0.72 0.160.24 0.32 0.400.48 0.560.64 0.720.800.88 Proportion of orange Proportion of orange Proportion of orange 2000 4000 6000 8001 00081 00071 0009 0009 12000 18000
Again, without performing any calculations,' what would be less likely to occur: Obtaining a sample proportion of 0.60 or larger when randomly selecting a sample of size n = 25, or obtaining a sample proportion of 0.60 or larger when randomly selecting a sample of size n = 50? Please explain
Transcribed Image Text:Again, without performing any calculations,' what would be less likely to occur: Obtaining a sample proportion of 0.60 or larger when randomly selecting a sample of size n = 25, or obtaining a sample proportion of 0.60 or larger when randomly selecting a sample of size n = 50? Please explain
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