Question

1. Suppose that a population is asked whether they prefer baseball or another sport. Let p = .4 denote the proportion of the population that prefers baseball.
   1. Create a graphical summary of the population distribution.
   2. Suppose that a sample of size n=60, drawn from this population, contains 22 individuals that prefer baseball to other sports. Create a graphical summary of this sample data distribution.
   3. Use the criteria referenced in Section 6.1 to verify that the sampling distribution of sample proportions drawn from this population is approximately normal.
   4. Using p = .4 and n=60, write down the center (“mean”) and the standard deviation of the sampling distribution of sample proportions using the information in Section 6.1.
   5. It’s not at all easy to draw the actual sampling distribution especially with a sample size of n=60, but we can get a lot of information about the sampling distribution using (i) approximations by simulations and (ii) approximations by normal distributions. Please create the following approximations.

Answer 1

Answer: from the given data, a) the graphical summary of the population distribution is: 7 normal mean -0.4 st-dev = 0.0645 6 5 Density 6.2 0-3 0.4 0.5 0.6 X en-60 & X-22 the goaphical summary of the sample data distribution ºs. Normal mean = 0-3667 st der=0.0645 6 Density 5 4 2 1 0-2 0.3 0.4 OS 0-6 c) ve vify that the sampling distribution of sample proportions drawn from this population is approximately normal. n*P = 60*P 22 P= DP = 60* 22 60 -22 Zlo DC1-P) = 60 (1-2%)- 38210 the sampling distribution of sample pro portions drawn from this population is appooximately normala d) p=0.4 and on=60. mean =p=foru PCI-P) 0.4(1-0.4) Standard deviation : 0.0632 60 Thank you