Download μ = 10 H

1.
An automobile manufacturer claims that the average gas mileage of a new model is 35 miles per gallon (mpg). A consumer group
is skeptical of this claim and thinks the manufacturer may be overstating the average gas mileage. If  represents the true average
gas mileage for this new model, which of the following gives the null and alternative hypotheses that the consumer group should
test?
H a :   35 mpg
(A) H 0 :   35 mpg
(B) H 0 :   35 mpg
(C) H 0 :   35 mpg
(D) H 0 :   35 mpg
H a :   35 mpg
H a :   35 mpg
H a :   35 mpg
(E) H 0 :   35 mpg
H a :   35 mpg
2.
Which of the following is a criterion for choosing a t-test rather than a z-test when making an inference about the mean of a
population?
(A) The standard deviation of the population is unknown.
(B) The mean of the population is unknown.
(C) The sample may not have been a simple random sample
(D) The population is not normally distributed.
(E) The sample size is less than 1.00.
3.
In a test of the null hypothesis H 0 :   10 against the alternative hypothesis H a :   10 a sample from a normal population
produces a mean of 13.4. The z -score for the sample is 2.12 and the p-value is 0.017. Based on these statistics, which of the
following conclusions could be drawn?
(A) There is reason to conclude that   10
(B) Due to random fluctuation, 48.3 percent of the time a sample produces a mean larger than 10.
(C) 1.7 percent of the time, rejecting the alternative hypothesis is in error.
(D) 1.7 percent of the time, the mean is above 10.
(E) 98.3 percent of the time, the mean is below 10.
4.
The process of producing pain-reliever tablets yields tablets with varying amounts of the active ingredient. It is claimed that the
average amount of active ingredient per tablet is at least 200 milligrams. The Consumer Watchdog Bureau tests a random sample
of 70 tablets. The mean content of the active ingredient for this sample is 194.3 milligrams, while the standard deviation is 21
milligrams. What is the approximate p -value for the appropriate test?
(A) 0.012
(B) 0.024
(C) 0.050
(D) 0.100
(E) 0.488
5.
A manufacturer of balloons claims that p, the proportion of its balloons that burst when inflated to a diameter of up to 12 inches,
is no more than 0.05. Some customers have complained that the balloons are bursting more frequently. If the customers want to
conduct an experiment to test the manufacturer's claim, which of the following hypotheses would be appropriate?
(A) H 0 : p  0.05 , H a : p  0.05
(B) H 0 : p  0.05 , H a : p  0.05
(C) H 0 : p  0.05 , H a : p  0.05
(D) H 0 : p  0.05 , H a : p  0.05
(E) H 0 : p  0.05 , H a : p  0.05
6.
A consulting statistician reported the results from a learning experiment to a psychologist. The report stated that on one particular
phase of the experiment a statistical test result yielded a p-value of 0.24. Based on this p-value, which of the following
conclusions should the psychologist make?
(A) The test was statistically significant because a p-value of 0.24 is greater than a significance level of 0.05.
(B) The test was statistically significant because p = 1 - 0.24 = 0.76 and this is greater than a significance level of 0.05.
(C) The test was not statistically significant because 2 times 0.24 = 0.48 and that is less than 0.5.
(D) The test was not statistically significant because, if the null hypothesis is true, one could expect to get a test statistic at least
as extreme as that observed 24% of the time.
(E) The test was not statistically significant because, if the null hypothesis is true, one could expect to get a test statistic at least
as extreme as that observed 76% of the time.
7.
The analysis of a random sample of 500 households in a suburb of a large city indicates that a 98 percent confidence interval for
the mean family income is ($41,300, $58,630). Could this information be used to conduct a test of the null hypothesis Ho:
  40 , 000 against the alternative hypothesis Ha:   40 , 000 at the  = 0.02 level of significance?
(A) No, because the value of  is not known.
(B) No, because it is not known whether the data are normally distributed.
(C) No, because the entire data set is needed to do this test.
(D) Yes, since $40,000 is not contained in the 98 percent confidence interval, the null hypothesis would be rejected in favor of
the alternative, and it could be concluded that the mean family income is significantly different from $40,000 at the  = 0.02
level.
(E) Yes, since $40,000 is not contained in the 98 percent confidence interval, the null hypothesis would not be rejected, and it
could be concluded that the mean family income is not significantly different from $40,000 at the  = 0.02 level.
8.
As lab partners, Sally and Betty collected data for a significance test. Both calculated the same z-test statistic, but Sally found the
results were significant at the  = 0.05 level while Betty found that the results were not. When checking their results, the women
found that the only difference in their work was that Sally had used a two-sided test, while Betty used a one-sided test. Which of
the following could have been their test statistic?
(A) -1.980
(B) -1.690
(C) 1.340
(D) 1.690
(E) 1.780
9. A one-tailed hypothesis test is conducted at the  = .05 level of significance resulting in a P-value =.032. Which of the following
conclusions is not valid?
(A) A two-tailed hypothesis test for the same situation would indicate a non-significant result.
(B) The probability of making a correct decision is .032.
(C) If the sample and population values stayed the same and the sample size increased, then the P-value would decrease.
(D) We expect the 95% confidence interval of the sample result would contain the expected population value.
(E) All of these are valid conclusions.
10. A two-tailed hypothesis ( = .05) of a population mean has a P-value of .072. Which of the following conclusions is valid?
(A) The null hypothesis should be accepted.
(B) The null hypothesis should be rejected.
(C) A one-tailed test of the null hypothesis using the same sample will be significant.
(D) The P-value of 0.072 indicates the probability that the null hypothesis is false.
(E) None of these is a valid conclusion.
11. A test is conducted to determine if a random sample of 100 fish whose mean length is 53 centimeters provides evidence that the
expected mean length of 50.5 centimeters is low. The P-value of the appropriate test is .072. This P-value represents the
probability that
(A) the corresponding confidence interval captures the expected mean of 50.5.
(B) the sample result causes an error in the expected result.
(C) a sample of size 100 would have a mean of 53 centimeters when the true mean is 50.5 centimeters.
(D) a sample of size 100 would provide a more accurate mean than the expected value of the mean.
(E) None of these is correct.
12. Which of the following is the reason that the conditions dealing with np and n(1 - p) are included in assumptions for z-tests for
proportions and differences of proportions?
(A) np must be greater than 30 in order for the Central Limit Theorem to apply.
(B) Small samples cannot be used with z-tests.
(C) z-tests should not be used on highly skewed sampling distributions.
(D) The conditions address the issue of the value of the mean of the sampling distribution.
(E) None of these is the reason for these conditions.
13. The test statistic from a two-tailed hypothesis test of the mean of the differences of a matched pair study of pre- and post-tests of
arithmetic for a class of 3rd graders produces a P-value of .12. Suppose that the level of significance is .02. Which of the
following statements is not true?
(A) The P-value is the probability of a sample yielding this difference or a larger difference when the null hypothesis is true.
(B) The 98% confidence interval of the mean difference of the population includes the value of 0.
(C) A one-tailed test with the same sample information will generate a P-value of .06.
(D) A two-sample test of the data will produce the same P-value as this matched pair t-test.
(E) All of these are true statements.
14. A sample of 100 engineers in a large consulting firm indicated that the mean amount of time they spend reading for pleasure each
week is 1.4 hours. Three interns independently calculate different confidence intervals of the true mean amount of time for all of
the engineers in the company. The confidence intervals of the interns were A: (.17, 2.63); B: (.554, 2.446); and C: (1.167, 1.633).
Which conclusion is valid?
(A) All are calculated correctly with different levels of confidence.
(B) A and C have reasonable intervals but B does not.
(C) A and B have reasonable intervals but C does not.
(D) B and C have reasonable intervals but A does not.
(E) None of these intervals is reasonable.
15. Which of the following is the reason that the tests for difference of proportions and difference of means include a requirement of
independent samples?
(A) The sample proportions or means could be skewed if the samples were not independent.
(B) The tests do not apply to samples from the same population.
(C) The samples will not be simple random samples unless they are independent.
(D) Variances from independent samples can be combined easily whereas variances from dependent samples are not as easily
combined.
(E) None of these is the reason for this requirement.
16. In a test of the equality of the proportions of men and women who take prescription drugs every day, the null hypothesis is that the
difference is 0. If the P-value indicates that the null hypothesis should be rejected, which of the following statements is not
justified?
(A) The test was two-tailed.
(B) The test statistic is in the rejection region for the test.
(C) The test statistic is more extreme than the critical value of the sampling distribution for the appropriate level of significance.
(D) The conclusion does not address the truth of the alternative hypothesis.
(E) The P-value indicates that it is unlikely that a sample similar to the one in question would have this difference or a more
extreme difference if the actual difference is 0.
17. The decision between a z-test for a population mean or a t-test for a population mean is based on
(A) the sample size.
(B) whether the samples are simple random samples or not.
(C) the shape of the distribution from which the samples are taken.
(D) the size of the standard deviation of the sample.
(E) None of the above.
18. A company claims that their battery lasts 52.5 hours in continuous use in a flashlight. A simple random sample of batteries yields a
sample mean life of 48.9 hours with a standard deviation of 5.2 hours. A computer calculates a test statistic of t = -1.832 and a Pvalue of 0.1167. If the test utilizes the degrees of freedom of 71, then the best estimate of the sample size is
(A) 71
(B) 72
(C) 73
(D) 74
(E) There is not sufficient information to deter mine the number of batteries in the sample
19. The P-value of a two-tailed t-test for a population mean is .064 when the level of significance is .05. Which of the following
statements are true?
I. A one-sided t-test using the same data would indicate a significant result.
II. The mean in the null hypothesis is true.
III. Even if the test indicates a significant result, it may not indicate an important result in the context of the problem.
(A) I only
(B) I and II
(C) I, II, and III
(D) I and III
(E) III only
20. A high school principal includes the following statement in a parent newsletter: "Our students continue to excel as evidenced by
the fact that the average grade given on the first semester report cards was 83.4, which is a solid B!" The Student Council
conducts a simple random sample of 20 students and determines that their average grade was 80.6 with a standard deviation of
11.7. A z-test for the population mean using H0:  = 83.4 concluded that this sample did not provide sufficient evidence to doubt
the principal's claim at the 5% level. Why was the Student Council's conclusion invalid?
(A) They needed to do a stratified sample so that all classes in the high school were equally represented.
(B) The number of students did not meet the minimum sample size requirement for a z-test.
(C) The sample standard deviation was too large for the population to be normal.
(D) The standard deviation of the population was not known.
(E) The conclusion is valid.
21. A set of 150 data values from a breeding experiment is tested against a genetic model using a chi-square test at the 2% level of
significance. If there are 5 categories of offspring listed and the chi-square value is 11.58, which of the following conclusions are
valid?
I. The data are significant and the hypothesis that the data fits the model should be rejected.
II. The data are not significant and we fail to reject the hypothesis that the data fits the model.
III. The data would not be significant if the test were conducted at the 1% level of significance.
(A) I only
(B) II only
(C) I and III
(D) II and III
(E) There is insufficient data to make any conclusion.
22. A marketing study determined that 55% of randomly selected adults preferred their company's new type of crackers. Earlier it was
anticipated that adults would be evenly split on their preference for the company's new product. If a hypothesis test for the
population proportion is conducted, what is the standard error that will be used in the test?
(A) 0.012
(B) 0.025
(C) 0.051
(D) 0.076
(E) There is insufficient information to calculate the standard error for the test.
Answers
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
D
A
A
A
B
D
D
A
D
C
C
C
D
B
D
A
E
B
D
D
D
E