Stats Help Q9 Thank you Each student in a large statistics c

Stats Help! (Q#9)

Thank you!

Each student in a large statistics class of 600 students is asked to toss a fair coin 100 times, count the resulting number of Heads, and construct a 0.95-level confidence interval for the probability of Heads. Assume that each student uses a fair coin and constructs the confidence interval correctly. True or False: We would expect approximately 570 of the confidence intervals to contain the number 0.5. Explain. Mt. Wrightson, the fifth highest summit in Arizona and the highest in Pima County, has a reputed elevation of 9453 feet. To amuse its members, the Southern Arizona Hiking Club (SAHC) decides to construct its own confidence interval for mu, the true elevation of Mt. Wrightson\'s summit. SAHC acquires an altimeter whose measurements will have an exerted value of mu with a standard deviation of 6 feet. How many nv^ureraents should SAHC plan to take if it wants to construct a 99-level confidence interval for mu that has a length of 2 feet? Professor Johnson is interested in the probability that a certain type

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.005  
      
Using a table/technology,      
      
z(alpha/2) =    2.575829304  
      
Also,      
      
s = sample standard deviation =    6  
E = margin of error =    2  
      
Thus,      
      
n =    59.71406941  
      
Rounding up,      
      
n =    60   [ANSWER]