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AP Statistics
AP Review – Hypothesis Test with Means
1) Which of the following are true statements?
I.
The p-value of a test is the probability of obtaining a result
as extreme or more extreme as the one obtained assuming the
null hypothesis is true.
II. If the p-value for a test is .015, the probability that the null
hypothesis is true is .015.
III. When the null hypothesis is rejected, it is because it is not
true.
a) I only
d) I and III
b) II only
e) None of the above gives the
c) III only
complete set of true responses.
2) A coffee-dispensing machine is supposed to deliver 8 ounces of
liquid into each paper cup, but a consumer believes that the actual
amount is less. As a test he plans to obtain a sample of 36 cups of the
dispensed liquid and, if the mean content is less than 7.75 ounces, to
reject the 8-ounce claim. If the machine operates with a standard
deviation of 0.9 ounces, what is the probability that you obtain a result
as extreme or more extreme as that observed?
a) .0475
d) .3897
b) .0950
e) .4525
c) .1500
3) Which of the following statements are true?
I.
It is helpful to examine your data before deciding whether to
use a one-sided or a two-sided hypothesis test.
II. If the p-value is .05, the probability that the null hypothesis
is correct is .05.
III. The larger the p-value, the more evidence there is against the
null hypothesis.
a) I only
d) I and III
b) II only
e) None of the above gives the
c) III only
complete set of true responses.
4) Which of the following are true statements?
I.
The alternative hypothesis is stated in terms of a sample
statistic.
II. A large p-value is evidence for the alternative hypothesis.
III. If a sample is large enough, the necessity for it to be a simple
random sample is diminished.
a) I only
d) I and III
b) II only
e) None of the above gives the
c) III only
complete set of true responses.
5) You conduct a hypothesis test and find a p-value of .025. Which of
the following is true?
a) You can reject H0 at α = .01.
b) You can reject H0 at α = .05.
c) You can accept H0 at α = .05.
d) You can say the probability that H0 is true is .025.
e) None of these are true.
6) It is believed that using a new fertilizer will result in a yield of 1.6
tons per acre. A botanist carries out a two-tailed test on a field of 64
acres. Determine the p-value if the mean yield per acre in the sample
is 1.72 tons with a standard deviation of 0.4 tons. What is the
conclusion at a level of significance of 10% 5% 1%
a) p-value = .0097, and so the 1.6 ton claim should be disputed at all
three of these levels
b) p-value = .0194, and so the 1.6 ton claim should be disputed at the
10% and 5% level but not at the 1% level
c) p-value = .0097, and so the 1.6 ton claim should be disputed at the
10% level, but not at the 5% and 1% levels
d) p-value = .0194, and so the 1.6 ton claim should be disputed at the
1% level, but not the 10% and 5% levels
e) p-value = .0097, and so there is not enough evidence to dispute the
1.6 ton claim at any of the three levels
Answers:
1-D, 2-A, 3-A, 4-E, 5-B, 6-B. 7-D, 8-C, 9-B, 10-C, 11-E, 12-D
7) An automotive company executive claims that a mean of 48.3 cars
per dealership are being sold each month. A major stockholder
believes this claim is high and runs a test by sampling 30 dealerships.
What conclusion is reached if the sample mean is 45.4 cars with a
standard deviation of 15.4?
a) There is sufficient evidence to prove the executive’s claim is true.
b) There is sufficient evidence to prove the executive’s claim is false.
c) The stockholder has sufficient evidence to reject the executive’s
claim.
d) The stockholder does not have sufficient evidence to reject the
executive’s claim.
e) There is not sufficient data to reach any conclusion.
8) Margaret’s Sock Emporium sells hand-knit wool socks. Margaret
claims the mean amount of wool per pair is 2 ounces. You take a
random sample of 20 socks and find that the mean weight is 1.9
ounces with standard deviation of 0.2 ounces. Assume that the amount
of wool is normally distributed, what is the p-value for getting a
sample mean of 1.9 or less?
a) 0.05
d) 0.013
b) 0.01
e) –2.24
c) 0.019
9) The El Burrito food chain is concerned that customers will be
dissatisfied if its Grande Bean Burrito is averaging less than 1.2
pounds. But if its burrito is averaging more than 1.2 pounds its profits
will suffer. A random sample of 42 burritos had a mean of 1.4 pounds
with a standard deviation of 0.5 pounds. Based on the test of the
hypotheses H0: μ = 1.2 versus Ha: μ > 1.2, which of these statements
represents a logical conclusion?
a) Customers will be dissatisfied with smaller burritos.
b) The company’s profits may suffer because the burritos are too
large.
c) The average weight isn’t statistically different from the expected
burrito weight.
d) The average weight of burritos is 99% higher than expected.
e) None of the above statements are correct.
10) A farmer wants to know whether a new fertilizer has increased the
mean weight of his apples. With the old fertilizer, the mean weight
was 4.0 ounces per apple. The weights of apples are approximately
normally distributed. A random sample of 16 apples has a weight of
4.3 ounces and a standard deviation of 0.6 ounces. Which of the
following gives the p-value for this test?
a) P(z > 2)
d) P(t < 2) with 15 degrees of freedom
b) P(z < 2)
e) P(t > 2) with 16 degrees of freedom
c) P(t > 2) with 15 degrees of freedom
11) Which of the following statements correctly describes the relation
between a t-distribution and a standard normal distribution?
a) The standard normal distribution is centered at 0, while the tdistribution is centered at (n – 1).
b) As the sample increases, the difference in the proportion of area in
the tails between the t-distribution and the standard normal
distribution increases.
c) The standard normal distribution is just another name for the tdistribution.
d) The standard normal distribution has more area in the tails than the
t-distribution.
e) The standard normal distribution has less area in the tails than the tdistribution.
12) In a chemistry class, the teacher wishes to see if there is a
difference in the grades for first and second semesters. Which of the
following is a correct interpretation for these hypotheses?
H0: μ (2nd -1st) = 0 versus
Ha: μ (2nd -1st) > 0
a) The mean 1st semester grade is 0 vs. the mean 1st semester grade >0
b) The mean 2nd semester grade is 0 vs. the mean 2nd semester grade
>0
c) The mean difference between the 1st & 2nd semester grades = 0 vs.
the mean 1st semester grade is > the mean 2nd semester grade
d) The mean difference between the 1st & 2nd semester grades = 0 vs.
the mean 2nd semester grade is > the mean 1st semester grade
e) The mean difference between the 1st & 2nd semester grades = 0 vs.
the mean 1st semester grade is  the mean 2nd semester grade