Mr. Rogers  AP Statistics Objectives

AP Statistics Practice Test Sampling Distributions Confidence Intervals Chapt 9 & 10 

1  )  According to the central limit theorem, the sampling distribution: 1) gets narrower or has less variability and 2) more closely resembles a normal distribution as sample size increases..  
2  )  The average height all monkeys is 48 with a standard deviation of 2 inches. What is the standard deviation of monkey heights for the sampling distribution of size ten? SE = 2 / (10)^{0.5}  
3  )  What effect does population size have on the mean and standard deviation of a sampling distribution? no effect on the mean or std dev  
4  )  Generally a statistic is used for estimating a corresponding parameter.  
5  )  Indicate which of the following can fit the binomial setting. Y=yes, N=no  


no, p is not constant If 45% of all students wore Bob's Jumpy Shoes in 1978 what is the probability of finding a random sample of 20 students that wear Bob's Jumpy Shoes the year 2057?  

6  )  If the width of a confidence interval triples, what also had to happen to the margin of error? 3x  
7  ) 
If the sample size is increased by a factor of 2, what is the effect on the
margin of error? new ME change = (1 / (2)^{0.5})*(old ME) = 0.707(old ME) 


8  ) 
If the confidence level is changed from 80% to 95% what is the effect on the
margin of error?
% change = [(1.961.28) / 1.28]*100% = 53% 

9  )  Which type(s) of error(s) will the margin of error account for? Random sampling error or variability  
10  )  What is the z* for a confidence level of 85%? 1.44  
11  )  Which types of studies can make use of confidence intervals? SRS  
12 
What is the minimum sample size for determining the mean length of widgets
in a manufacturing industry to a margin of error = plus or minus .2 given a
90% confidence interval and a standard deviation = 3. ME = Z* ( σ_{p}/ n^{0.05}) n (ME) = Z* ( σ_{p}) n^{0.05} = (Z* σ_{p}) / (ME) n = [(Z* σ_{p}) / (ME)]^{2} n = [1.64(3) / (0.2)]^{2} n = 605.1 rounding up, use 606 

13  )  Which is more accurate, a margin of error with a confidence level of 65% or a margin of error with a confidence interval of 90%? Can't tell.  
14  )  For an 80 % confidence interval, we are confident that _______________ .  
80 % of confidence intervals constructed around a sample statistic will contain the population parameter. 