3321 PRACTICE QUESTIONS FOR TEST 2
1.
Which of the following statements about the sampling distribution
of the sample mean is incorrect?
a. The sampling distribution of the sample mean is approximately
normal whenever the sample size is sufficiently large (n ≥ 30).
b. The sampling distribution of the sample mean is generated by
repeatedly taking samples of size n and computing the sample
means.
c. The mean of the sampling distribution of the sample mean is
equal to µ.
d. The standard error of the sampling distribution of the sample
mean is equal to σ.
2.
The owner of a fish market has an assistant who has determined
that the weights of catfish are normally distributed, with mean of
3.2 pounds and standard deviation of 0.8 pound. If a sample of 16
fish is taken, what would the standard error of the mean weight
equal?
a. 0.003
b. 0.050
c. 0.200
d. 0.80
3
A Type II error is committed when
a. we reject a null hypothesis that is true.
b. we don't reject a null hypothesis that is true.
c. we reject a null hypothesis that is false.
d. we don't reject a null hypothesis that is false.
4.
If an economist wishes to determine whether there is evidence that
average family income in a community exceeds $25,000
a. either a one-tailed or two-tailed test could be used with
equivalent results.
b. a one-tailed test should be utilized.
c. a two-tailed test should be utilized.
d.None of the above.
5.
How many Kleenex should the Kimberly Clark Corporation package of
tissues contain? Researchers determined that 60 tissues is the
average number of tissues used during a cold. Suppose a random
sample of 100 Kleenex users yielded the following data on the
number of tissues used during a cold: X-bar= 52, s = 22. Give the
null and alternative hypotheses to determine if the number of
tissues used during a cold is less than 60.
a. H0: µ ≤ 60 and H1: µ > 60.
b. H0: µ ≥ 60 and H1: µ < 60.
c. H0: X-bar ≥ 60 and H1: X-bar < 60.
d. H0: X-bar = 52 and H1: X-bar ≠ 52.
6.
How many Kleenex should the Kimberly Clark Corporation package of
tissues contain? Researchers determined that 60 tissues is the
average number of tissues used during a cold. Suppose a random
sample of 100 Kleenex users yielded the following data on the
number of tissues used during a cold: X-bar = 52, s = 22. Using the
sample information provided, calculate the value of the test
statistic.
a. z = (52 - 60)/22
b. t = (52 - 60)/(22/100)
c. t = (52 - 60)/(22/1002)
d. z = (52 - 60)/(22/10)
7.
How many Kleenex should the Kimberly Clark Corporation package of
tissues contain? Researchers determined that 60 tissues is the
average number of tissues used during a cold. Suppose a random
sample of 100 Kleenex users yielded the following data on the
number of tissues used during a cold: X-bar = 52, s = 22. Suppose
the test statistic does fall in the rejection region at а = 0.05.
Which of the following conclusions is correct?
a. At а = 0.05, we do not reject H0.
b. At а = 0.05, we reject H0.
c. At а = 0.05, we accept H0.
d. At а = 0.10, we do not reject H0.
8.
We have created a 90% confidence interval for µ with the result
(110, 115). What conclusion will we make if we test H0: µ = 120
versus H1: µ ≠ 120 at а = 0.05?
a. Reject H0 in favor of H1.
b. Accept H0 in favor of H1.
c. Fail to reject H0 in favor of H1.
d. We cannot tell what our decision will be from the information
given.
9.
We have created a 90% confidence interval for µ with the result
(110, 115). What conclusion will we make if we test H0: µ = 120
versus H1: µ ≠ 120 at а = 0.10?
a. Reject H0 in favor of H1.
b. Accept H0 in favor of H1.
c. Fail to reject H0 in favor of H1.
d. We cannot tell what our decision will be from the information
given.
10. If, as a result of a hypothesis test, we reject the null
hypothesis when it is false, then we have committed
a. a Type II error.
b. a Type I error.
c. no error.
d. an acceptance error.
11. The owner of a local nightclub has recently surveyed a random
sample of n = 250 customers of the club. She would now like to
determine whether or not the mean age of her customers is over 30.
If so, she plans to alter the entertainment to appeal to an older
crowd. If not, no entertainment changes will be made. The
appropriate hypotheses to test are:
a. H0: µ ≥ 30 versus H1: µ < 30.
b. H0: µ ≤ 30 versus H1: µ > 30.
c. H0: X-bar ≥ 30 versus H1: X-bar < 30.
d. H0: X-bar ≤ 30 versus H1: X-bar > 30.
12. Suppose Z has a standard normal distribution with a mean of 0 and
standard deviation of 1. The probability that Z is less than -2.20
is __________.
13. The amount of time necessary for assembly line workers to complete
a product is a normal random variable with a mean of 15 minutes
and a standard deviation of 2 minutes. The probability is
__________ that a sample of 64 products has a mean assembly time
of less than 20 minutes.
14. At a computer manufacturing company, the actual size of computer
chips is normally distributed with a mean of 1 centimeter and a
standard deviation of 0.1 centimeter. A random sample of 12 computer
chips is taken. What is the probability that the sample mean will be
between 0.99 and 1.01 centimeters?
15. The amount of pyridoxine (in grams) per multiple vitamin is
normally distributed with µ= 110 grams and σ = 25 grams. A sample
of 25 vitamins is to be selected. What is the probability that the
sample mean will be between 100 and 120 grams?
16. The amount of time required for an oil and filter change on an
automobile is normally distributed with a mean of 45 minutes and a
standard deviation of 10 minutes. A random sample of 16 cars is
selected. So, 90% of the sample means will be greater than what
value?
17. The amount of bleach a machine pours into bottles has a mean of 36
oz. with a standard deviation of 0.15 oz. Suppose we take a random
sample of 36 bottles filled by this machine. The probability that
the mean of the sample is between 35.94 and 36.06 oz. is
__________.
18. A prison official wants to estimate the proportion of cases of
recidivism. Examining the records of 250 convicts, the official
determines that there are 65 cases of recidivism. A 99% confidence
interval for the proportion of cases of recidivism would go from
__________ to __________.
TABLE 6-8
A hotel chain wants to estimate the average number of rooms rented
daily in each month. The population of rooms rented daily is assumed
to be normally distributed for each month with a standard deviation of
24 rooms.
19. Referring to Table 6-8, during February, a sample of 25 days has a
sample mean of 37 rooms. Use this information to calculate a 92%
confidence interval for the population mean.
TABLE 7-4
A drug company is considering marketing a new local anesthetic. The
effective time of the anesthetic the drug company is currently
producing has a normal distribution with an average of 7.4 minutes
with a standard deviation of 1.2 minutes. The chemistry of the new
anesthetic is such that the effective time should be normal with the
same standard deviation, but the mean effective time may be lower. If
it is lower, the drug company will market the new anesthetic;
otherwise, they will continue to produce the older one. A hypothesis
test will be done to help make the decision.
20. Referring to Table 7-4, for a test with a level of significance of
0.10, the critical value would be ________.
TABLE 7-4
21. Referring to Table 7-4, a sample of size 36 results gave a sample
mean of 7.1. If the level of significance had been chosen as 0.05,
the null hypothesis would be rejected.
a. True
b. False