STAT200 Quiz 3 2016

Multiple-choice: Choose only ONE answer in each question.

There are 27 problems for 3 points each.

01: An assumption made about the value of a population parameteris called a

A. conclusion
B. confidence
C. significance

D. hypothesis

E. none of the above

02: The p-value is a probability that measures the support or lack of support for the

A. alternative hypothesis

B. null hypothesis
C. either the null or the alternative hypothesis
D. sample statistic
E. none of the above

03: In hypotheses testing if the null hypothesis has been rejected when the alternative hypothesis is true, then
A. a Type I error has been committed

B. a Type II error has been committed

C. either a Type I or Type II error has been committed
D. the correct decision has been made

E. none of the above

04. In a hypothesis testing procedure, ? is

A. the level of significance
B. the level of confidence
C. the critical value
D. the probability of Type I error
E. both A and D

05: In a one-tail, left-tail z-test, the test statistic is z = -2.01. The p-value is

A. 0.0179
B. 0.9778
C. 0.0222
D. 0.0174
E. none of the above

06. In a two-tail hypothesis test, the test statistic is determined to be z = -2.50. The p-value for this test is

A. 0.0062
B. 0.4938
C. 0.0031
D. -0.0124
E. 0.0124

07: In a two-tail t-test, the test statistic t = -2.89 and the sample size is 30. The p-value is

A. 0.9928
B. 0.0019
C. 0.0038
D. 0.0036
E. 0.0072

08. In one-tail, left-tailt-test, the test statistic t = -1.58 and the sample size is 23. The p-value is

A. 0.0571

B. 0.1284
C. 0.0642

D. -0.0642
E. none of the above

09. A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. If the machine overfills or under fills then it must be shut down and readjusted. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is

A. H₀: µ < 12 H_A: µ ? 12

B. H₀: µ = 12 H_A: µ > 12

C. H₀: µ ? 12 H_A: µ = 12

D. H₀: µ = 12 H_A: µ ? 12

E. H₀: µ = 12 H_A: µ < 12

10: What kind of Alternative Hypothesis is used in the figure below?

A. H_A: µ = µ₀
B. H_A: µ ? µ₀
C. H_A: µ > µ₀
D. H_A: µ < µ₀
E. none of the above

11. Which type of Alternative Hypothesis is used in the figure below?

A. H_A: µ = µ₀
B. H_A: µ ? µ₀
C. H_A: µ > µ₀
D. H_A: µ < µ₀
E. None of the above

Use the following to answer the next four questions.

The weights of small fish sold at a market are normally distributed. A random sample of 15 fish yields a mean weight of 3.8 ounces with a sample standard deviation s = 0.5 ounces. At the .05 level of significance, perform a hypothesis test to see if the true mean weight is less than 4 ounces. Use ? = 0.05.

12. The correct null and alternative hypotheses are
A.H_0:µ ? 4; H_A: µ > 4
B. H_0:µ = 4; H_A: µ < 4
C.H_0:µ > 4; H_A: µ = 4
D.H_0:µ < 4; H_A: µ = 4
E.H_0:µ = 4; H_A: µ ? 4

13. The correct calculated value of the test statistic is
A. t= -0.40.
B. t= 0.40.
C. t= -1.55.
D. t= 1.55.
E. t= 2.79.

14. The correct critical t-value is

A. 1.761
B. -1.761
C. -1.753
D. 2.145
E. -2.145

15. Thecorrect p-value is

A. 0.1434
B. 0.0717
C. 0.0709
D. 0.0606
E. none of the above

16. The correct conclusion at the ? = 0.05 level of significance is

A.Fail to reject the null hypothesis.
B.Reject the null hypothesis.
C.Evidence suggests that the mean weight is less than 4 ounces.
D.Both A and C
E.Both B and C

Use the following to answer the next five questions.

An organization conducts a poll to determine the support the health care bill that just passed. In a random sample of 1000 adults surveyed, 498 responded “yes.” We would like to test if the proportion of respondents that support the health care bill is at least 50%.

17. Which of the following statements is true about this hypothesis test?

A. It is a two tail test about a proportion
B. It is a one tail test about a mean
C. It is a one tail test about a proportion
D. It is a two tail test about a mean
E. None of the above

18. The correct alternative hypothesis is

A.p = 0.50
B.p ? 0.50
C.p ? 0.50
D.p > 0.50
E.p < 0.50

19. The calculated test statistic value is

A.
B.
C.
D.
E. None of the above

20. The associate P-Value with the test statistic is

A. 0.0968.
B. 0.4483.
C. 0.9032.
D. 0.5517.
E. None of the above

21. At the ?= 0.01 level of significance, the correct conclusion is

A.Fail to reject the null hypothesis.
B.Reject the null hypothesis.
C.Evidence suggests that less than 50% of respondents support the bill.
D. Both A and C
E.Both B and C

Consider the following to answer the next five questions:

A consumer group was interested in comparing the operating time of cordless toothbrushes manufactured by two different companies. They took a random sample of toothbrushes from each company. Each toothbrush was charged overnight and the number of hours of use before needing to be recharged was recorded. The data are shown in the table. Assume normal distributions.

Do these samples indicate that there is a difference in the mean operating times between cordless toothbrushes manufactured by the two companies?

22. Which of the following statements is true?

A. This is a one tailed test of two dependent samples.
B. This is a two tailed test of two independent samples.
C. This is a one tailed test of two independent samples.
D. These samples are matched.
E. None of the above.

23. The correct Null and Alternative hypotheses are

A. H_0: µ₁- µ_{2 ?} 0 and H_A: µ₁- µ₂> 0
B. H_0: µ₁- µ_{2 ?} 0 and H_A: µ₁- µ₂< 0
C. H_0: µ₁- µ₂= 0 and H_A: µ₁- µ₂< 0
D. H_0: µ₁- µ₂= 0 and H_A: µ₁- µ₂? 0
E. None of the above

24. The correct value of the test statistic is

A. -1.49
B. -4.42
C. 2.56
D. 1.49
E. none of the above

25. The correct p-value is

A. 0.0681
B. -0.0681
C. 0.1362
D. 0.1616
E. none of the above

26. At ? = .05

A. we reject the null hypothesis.
B. we fail to reject the null hypothesis.
C. we can conclude that there is no significant difference between the mean operating times of cordless toothbrushes manufactured by the two companies.
D. Both A and C
E. Both B and C

27. If we were to construct a 95% confidence interval for the difference between the mean operating times of cordless toothbrushes manufactured by Company 1and Company 2, we would expect

A. the upper and lower limits to both be negative.
B. the upper and lower limits to both be positive.
C. that zero is not included in the interval.
D. that zero is included in the interval.
E. None of the above