Answer:
Step-by-step explanation:
Given that a statistician selected a random sample of 125 observations from a population with a known standard deviation equal to 16 and computed a sample mean equal to 77
We can use Z critical values since population std deviation is known. Also sample size >30
We find std error of mean =
Margin of error = Z critical value * 1.4311
Z critical values for 93% = 1.81
for 89% = 1.60
n Std error Z critical Conf interval
89%
125 1.4311 1.6 (74.71024 79.28976 )
93%
1.81 (74.409709 79.590291 )
We find that when confidence level increases interval width increses.
c) When sigma changes to 441, std error changes to
So we get
n Std error Z critical Conf interval
89%
441 0.7619 1.6 (75.781 78.219 )
93%
1.81 (75.621 78.37904)
d) When n = 625, std error changes to 16/25 = 0.64
n Std error Z critical Conf interval
89%
441 0.64 1.6 (75.976 78.024 )
93%
1.81 (75.842 78.1584)
When sample size increases, confidence interval width decreases.