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					Name: _____________________________________                                   4) Which of the following are true statements?
AP Statistics                                                                     I.    The alternative hypothesis is stated in terms of a sample
AP Review – Hypothesis Test with Means                                                  statistic.
                                                                                  II. A large p-value is evidence for the alternative hypothesis.
1) Which of the following are true statements?                                    III. If a sample is large enough, the necessity for it to be a simple
    I.    The p-value of a test is the probability of obtaining a result as             random sample is diminished.
          extreme or more extreme as the one obtained assuming the            a) I only                              d) I and III
          null hypothesis is true.                                            b) II only                             e) None of the above gives the
    II. If the p-value for a test is .015, the probability that the null      c) III only                            complete set of true responses.
          hypothesis is true is .015.
    III. When the null hypothesis is rejected, it is because it is not
          true.                                                               5) You conduct a hypothesis test and find a p-value of .025. Which of
a) I only                              d) I and III                           the following is true?
b) II only                             e) None of the above gives the         a) You can reject H0 at = .01.
c) III only                            complete set of true responses.        b) You can reject H0 at  = .05.
                                                                              c) You can accept H0 at  = .05.
2) A coffee-dispensing machine is supposed to deliver 8 ounces of liquid      d) You can say the probability that H0 is true is .025.
into each paper cup, but a consumer believes that the actual amount is        e) None of these are true.
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         6) It is believed that using a new fertilizer will result in a yield of 1.6
ounces, what is the probability that you obtain a result as extreme or        tons per acre. A botanist carries out a two-tailed test on a field of 64
more extreme as that observed?                                                acres. Determine the p-value if the mean yield per acre in the sample is
 a) .0475                                d) .3897                             1.72 tons with a standard deviation of 0.4 tons. What is the conclusion
 b) .0950                                e) .4525                             at a level of significance of 10% 5% 1%
 c) .1500                                                                     a) p-value = .0097, and so the 1.6 ton claim should be disputed at all
                                                                              three of these levels
3) Which of the following statements are true?                                b) p-value = .0194, and so the 1.6 ton claim should be disputed at the
    I.    It is helpful to examine your data before deciding whether to       10% and 5% level but not at the 1% level
          use a one-sided or a two-sided hypothesis test.                     c) p-value = .0097, and so the 1.6 ton claim should be disputed at the
    II. If the p-value is .05, the probability that the null hypothesis is    10% level, but not at the 5% and 1% levels
          correct is .05.                                                     d) p-value = .0194, and so the 1.6 ton claim should be disputed at the 1%
    III. The larger the p-value, the more evidence there is against the       level, but not the 10% and 5% levels
          null hypothesis.                                                    e) p-value = .0097, and so there is not enough evidence to dispute the
a) I only                              d) I and III                           1.6 ton claim at any of the three levels
b) II only                             e) None of the above gives the
c) III only                            complete set of true responses.
7) An automotive company executive claims that a mean of 48.3 cars per       10) A farmer wants to know whether a new fertilizer has increased the
dealership are being sold each month. A major stockholder believes this      mean weight of his apples. With the old fertilizer, the mean weight was
claim is high and runs a test by sampling 30 dealerships. What               4.0 ounces per apple. The weights of apples are approximately normally
conclusion is reached if the sample mean is 45.4 cars with a standard        distributed. A random sample of 16 apples has a weight of 4.3 ounces
deviation of 15.4?                                                           and a standard deviation of 0.6 ounces. Which of the following gives the
a) There is sufficient evidence to prove the executive’s claim is true.      p-value for this test?
b) There is sufficient evidence to prove the executive’s claim is false.     a) P(z > 2)                     d) P(t < 2) with 15 degrees of freedom
c) The stockholder has sufficient evidence to reject the executive’s         b) P(z < 2)                     e) P(t > 2) with 16 degrees of freedom
    claim.                                                                   c) P(t > 2) with 15 degrees of freedom
d) The stockholder does not have sufficient evidence to reject the
    executive’s claim.                                                       11) Which of the following statements correctly describes the relation
e) There is not sufficient data to reach any conclusion.                     between a t-distribution and a standard normal distribution?
                                                                             a) The standard normal distribution is centered at 0, while the t-
                                                                               distribution is centered at (n – 1).
8) Margaret’s Sock Emporium sells hand-knit wool socks. Margaret             b) As the sample increases, the difference in the proportion of area in
claims the mean amount of wool per pair is 2 ounces. You take a random         the tails between the t-distribution and the standard normal
sample of 20 socks and find that the mean weight is 1.9 ounces with            distribution increases.
standard deviation of 0.2 ounces. Assume that the amount of wool is          c) The standard normal distribution is just another name for the t-
normally distributed, what is the p-value for getting a sample mean of 1.9     distribution.
or less?                                                                     d) The standard normal distribution has more area in the tails than the
a) 0.05                                d) 0.013                                t-distribution.
b) 0.01                                e) –2.24                              e) The standard normal distribution has less area in the tails than the t-
c) 0.019                                                                       distribution.

                                                                             12) In a chemistry class, the teacher wishes to see if there is a
9) The El Burrito food chain is concerned that customers will be             difference in the grades for first and second semesters. Which of the
dissatisfied if its Grande Bean Burrito is averaging less than 1.2 pounds.   following is a correct interpretation for these hypotheses?
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           H0: (2nd -1st) = 0   versus       Ha: (2nd -1st) > 0
standard deviation of 0.5 pounds. Based on the test of the hypotheses
H0:  = 1.2 versus Ha:  > 1.2, which of these statements represents a       a) The mean 1st semester grade is 0 vs. the mean 1st semester grade >0
logical conclusion?                                                          b) The mean 2nd semester grade is 0 vs. the mean 2nd semester grade >0
a) Customers will be dissatisfied with smaller burritos.                     c) The mean difference between the 1 st & 2nd semester grades = 0 vs.
b) The company’s profits may suffer because the burritos are too large.          the mean 1st semester grade is > the mean 2nd semester grade
c) The average weight isn’t statistically different from the expected        d) The mean difference between the 1st & 2nd semester grades = 0 vs.
     burrito weight.                                                             the mean 2nd semester grade is > the mean 1st semester grade
d) The average weight of burritos is 99% higher than expected.               e) The mean difference between the 1 st & 2nd semester grades = 0 vs.
e) None of the above statements are correct.                                     the mean 1st semester grade is  the mean 2nd semester grade

				
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