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SMAM 314
Exam2n
Name_____________
1. Mark the following statements True T or False F. (6 points- 2each)
_____A. You have a data set. You do not know the population mean. Two hundred 95%
confidence intervals are calculated. About ten of them do not contain the true population
mean. You cannot tell which of the ten intervals contain the true population mean.
_____B. In performing a test of hypothesis the null hypothesis is rejected at 
Then the null hypothesis would be also rejected at 

C. When performing a t test you assume that the sample size is small , the
population is normal and that a historical value of the standard deviation is not available.
2. Pick the best choice. (4 points-2 each)
____A. You have a normal population with standard deviation 1. You are testing the
hypothesis H 0 =0 vs. H1 ­ 0 at =.01. The region of rejection is a. Z > 1.96
b. Z > 1.645, Z < –1.645 c. Z > 1.96, Z< –1.96 d. Z > 2.576, Z< –2.576 e. Z > 2.326,
Z<-2.326.
____B. Assume that X is a binomial random variable with n=100 and p=0.4. The random
variable Y is a normal random variable that approximates X. To calculate
P(46  X  57) making the continuity correction we must find a. P(45.5  Y  57.5)
b. P(45.5  Y  56.5) c. P(44.5  Y  56.5) d. P(46.5  Y  57.5) d. None of a,b,c or d.
3. One of the presidential candidates wants to estimate the proportion of voters that will
vote for him with a 98% confidence interval with error bound at most 0.1. How large a
sample does he need to take:
A. If in a preliminary poll of 100 voters 48 support him? (6 points)
B. If a preliminary estimate is not available?(6 points)
4. Use the Central Limit Theorem to do this problem.
The inside diameter of a piston rings manufactured by Parts Inc. is a random variable
with mean of 12 cm and standard deviation 0.04 cm.
A. If d represents the mean of a random sample of size 64 what is the mean and the
standard deviation of d ?(4 points)
B. What is the probability that for the sample of 64 piston rings the sample mean is
within .075 cm of 12 cm. In other words find P(11.925  d  12.075) .? (10 points)
C. Find a number c where P(12  c  x  12  c)  .10 . (10 points)
5. Suppose that only 40% of all drivers in a certain state wear a seatbelt. A random
sample of 1000 drivers is selected. Use the normal approximation to the binomial
distribution with the continuity correction to determine the probability that the number of
drivers in the sample that wear a seat belt is at most 420. (15 points)
6. A study was done on the propagation of an ultrasonic stress wave through a substance.
In particular the attenuation (the decrease in amplitude of the stress wave measured in
neper/cm) in fiber –glass reinforced plyester composites was measured . Attenuation
values are known to have a standard deviation of 0.25
2.6
2.5
2.2 2.0
2.1 2.3 2.6
A. Construct a 98% confidence interval for the true mean attenuation values. (8 points)
B. Interpret the confidence interval you found in Part A. (5 points)
C. Find the sample size required to estimate the true mean attenuation values to within
.10 using a 98% confidence interval. (6 points)
7. Holmes and Mergen (1992) studied a batch operation at a chemical plant. Production
personnel use a viscosity measurement for each 12-hour batch to monitor the process.
These are the viscosities for the past five batches.
14.8 15.2
14.9 14.6 14.1
A. Conduct a test of hypothesis to determine whether the mean viscosity exceeds 14.3
.Use points)
H0
H1
Assumptions
Region of rejection
Calculation
Reject or do not reject H0.
Conclusion
B. Would you reject H0 at Explain.(5 points)