The life in hours of a 75- watt light bulb is known to be normallydistributed wi

Question

The life in hours of a 75- watt light bulb is known to be normallydistributed with =15 hours. A random sample of n=20 bulbshas a mean life of x(bar)=1015 hours.
a) Construct a 95% two- sided confidence interval on the meanlife.
b) Construct a 99% two- sided confidence interval on the meanlife.
c) How do answers a) and b) compare to each other? Why?
d) Suppose we wanted the error in estimating the mean life for the95% two-sided confidence interval to be 5 hours, what sample sizeshould be used?
e) Suppose we wanted the error in estimating the mean life for the99% two-sided confidence interval to be 5 hours, what sample sizeshould be used?
f) How do answers d) and e) compare to each other? Why?

Explanation / Answer

sample size, n =20 mean , x(bar) =1015 hours. standard error, e = / n = 15/20 =3.354 degree of freedom, df = n- 1= 20-1 =19
a) at 95% confidence, i.e =0.05 for a two tail distributionand df = 19, t = 2.093 a 95% two- sided confidence interval on the mean life = x(bar)± (t*e) =1015 ± (2.093*3.354) =(1007.98, 1022.02)
b) at 99% confidence, i.e =0.01 for a two tail distributionand df = 19, t = 2.861 99% two- sided confidence interval on the mean life =x(bar)± (t*e) =1015 ± (2.861*3.354) =( 1005.4, 1024.6)
c) confidence interval in a) is less than in b) as confidencelevel increases, the confidence interval also increases.

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