Putting the Pieces Together

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, the standard deviation of the sampling distribution got smaller.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, andn= 150).Please answer the following questions based on what you see in the graphs below.

n = 25 n = 50 Mean = 0.50 n = 150 Mean = 0.50 Mean = 0.50 Standard deviation = 0.101 Standard deviation = 0.071 Standard deviation = 0.041 4000 3000 1800 3000 2000 2000 1200 1000 1000 600 O 0.12 0.24 0.36 0.48 0.60 0.72 0.84 0.16 0.24 0.32 0.40 0.48 0.56 0.64 0.72 0.80 0.32 0.36 0.40 0.44 0.48 0.52 0.56 0.60 0.64 0.68 Proportion of orange Proportion of orange Proportion of orange