Question

3) A random sample of 35 Hollywood movies made since the years 2010 had a mean length of 121.6 minutes, with a standard deviation of 20.4 minutes. a) Construct a 98% confidence interval for the true mean length of all Hollywood movies made since 2010. Interpret your answer. b) As of June 2013, three Ironman movies have been released, and their mean length is 127 minutes. Someone claims that the mean length of Ironman movies is less than the mean length of all Hollywood movies made since 2010. Does the confidence interval contradict this claim? Explain. c) If a 95% confidence interval was constructed with these data, would it be wider or narrower than the interval constructed in part a)? Explain.

Answer 1

4)

Sample Size,   n=   20
Sample Standard Deviation,   s=   2.9800
Confidence Level,   CL=   0.95
      
      
Degrees of Freedom,   DF=n-1 =    19
alpha,   α=1-CL=   0.05
alpha/2 ,   α/2=   0.025
Lower Chi-Square Value=   χ²1-α/2 =   8.907
Upper Chi-Square Value=   χ²α/2 =   32.852

confidence interval for std dev is       
lower bound= √[(n-1)s²/χ²α/2] =   √(19*2.98² / 32.8523)=   2.2663
      
      
upper bound= √[(n-1)s²/χ²1-α/2] =   √(19*2.98² / 8.9065)=   4.3525
      
there is 95% confidence that true std dev lies within confidence interval