Week 07 Exercises
Be sure to use the Microsoft Equation Editor to show answers and calculations.
1) What conditions are required to form a valid large-sample confidence interval for µ?
The values are independent and identically distributed with a finite variance.
2) A random sample of 90 observations produced a mean
and a standard deviation of
.
a) Find a 90% confidence interval for µ.
1.662(2.7)
1.662(2.7) 

, 25.9 
 25.9 
  (25.4 , 26.4)
90
90 

b) Find a 90% confidence interval for µ. (I will assume this says 95% to make it different
from the above question).
1.987(2.7)
1.987(2.7) 

, 25.9 
 25.9 
  (25.3 , 26.5)
90
90 

3) State the two problems (and corresponding solutions) that arise with using a small sample to
estimate µ.
I will take a guess at the two problems based on the other submitted questions. There are
many problems with small samples.
The standard deviation is unknown. Estimate the standard deviation with the sample standard
Week 07 Exercises
deviation.
The z test is inappropriate. Use the t test.
4) Suppose you have selected a random sample of
measurements from a normal
distribution. Compare the standard normal z-values with the corresponding t-values if you
were forming the following confidence intervals.
a) 80% confidence interval
Z = 1.282
T = 1.440
b) 90% confidence interval
Z = 1.645
T = 1.943
5) The following sample of 16 measurements was selected from a population that is
approximately normally distributed.
91 80 99 110 95 106 78 121 106 100 97 82 100 83 115 104
a) Construct an 80% confidence interval for the population mean and interpret the interval.
Average = 97.9375
Sample Standard Deviation = 12.646
Week 07 Exercises
1.341(12.646)
1.341(12.646) 

, 97.9375 
 97.9375 
  (93.7 , 102.2)
16
16


If many samples of size 16 are taken, about 80% of the averages will lie within the 80%
confidence interval.
b) Construct a 95% confidence interval for the population mean and interpret the interval.
2.131(12.646)
2.131(12.646) 

, 97.9375 
 97.9375 
  (91.2 , 104.7)
16
16


If many samples of size 16 are taken, about 95% of the averages will lie within the 95%
confidence interval.
c) Explain why the 80% confidence interval is narrower.
Because it requires less assurance that the mean lies within the interval. As the interval width
increases there is more assurance it will cover the mean.
1. Another name given to the sampling distribution of x is _ ______________.
A) median
B) mean
C) standard error of the median
D) standard error of the mean
Week 07 Exercises
None of the above is correct, finite sample distribution is one other name. I suspect this question did
not transfer correctly.
2.
The population parameter for standard deviation is ____ ___________.
A) p
B) p
C) σ2
D) σ
Answer: D
3. The sampling distribution of x is normally distributed, regardless of the size of the sample n.
This question sounds as though it is worded incorrectly, but I answered it as it stands.
A) True
B) False
Answer: B
4. Suppose a random sample of n = 25 measurements is selected from a population with the mean
µ = 100 and standard deviation σ = 25. Give the value of σ x
I will answer this question as though it read
x
A) 5
B) 1
C) 100
D) 4
25/5 = 5
Answer: A
5. A random sample of n = 68 observations is selected from population with µ = 19.6 and σ = 3.2.
Approximate P(x ≤ 19) by rounding to the hundredth place (second decimal place).
Week 07 Exercises
Judging by the answers, I will assume the question should read P ( x  19)
A) 0.06
B) 0.16
C) 0.18
D) 0.01
P( X  19)  P( Z 
Answer: A
19  19.6
3.2
68
)  P(Z  1.546)  0.06