Texas Eco578 Exam II 2015
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v There are 4 parts: Part A: Select the correct answer for the following questions (1-10) Part B: True/ False (11-20)
Part A: Multiple Choice (1–10)
____1. The cumulative probability distribution of a random variable X gives the probability that X is _______ to , some spacified value of X. a. Greater than or equal c. Less than or equal b. Equal d. None of the above _____2. The_______is the smallest level of significance at which can be rejected. a. Value of c. p value b. Probability of commiting of Type I error d. vale of 1 –
_____3. What is the probability of P(-1.4 < Z < 0.6)? a. 0.9254 c. 0.3427 b. 0.6449 d. 0.9788 _____4. By using the binomial table, if the sample size is 20 and p equals to 0.70, what is the value for P(X 18)? a. 0.0279 c. 0.1820 b. 0.0375 d. 0.1789 _____5. In a standard normal distribution, what is the area which lies between Z = -1.72 and Z = 2.53? a. 0.8948 c. 0.9516 b. 0.9123 d. 0.8604 _____6. A random sample of 60 items is taken producing a sample mean of 25 and a sample standard deviation of 12.25. What is the value for 95% confidence interval to estimate the population mean? a. 23.3844 24.8966 c. 28.3541 29.1359 b. 24.1144 25.8856 d. 25.8252 26.5478 _____7.You perform a hypothesis test about a population mean on the basis of the following information: the sampled population is normally distributed, s = 100, n = 25, = 225, ? = 0.05, Ha: µ > 220. The critical value of the test statistic is ______________ . a. 2.0639 b. 1.7081 c. 1.7109 d. 1.96 _____8.You perform a hypothesis test about a population mean on the basis of the following information: n = 50, = 100, ? = 0.05, s = 30, Ha: µ < 110. The computed value of the test statistic is _____________ . a. -2.3570 b. -1.645 c. 2.3570 d. 4.24264 _____9. What is score for P(Z ) = 0.0708? a. 1.47 c. 1.80 b. 1.35 d. 1.41 _____10. The random variable x has a normal distribution with = 40 and = 36. What is the value of x if P(X ) = 0.40? a. 47.86 c. 49.85 b. 41.50 d. 45.73 Part B: True or False (11-20) _____11. A normal distribution is a distribution of discrete data that produces a bell-shaped. _____12. The mean of the discrete probability distribution for a discrete random variable is called its expected value. _____13. A random variable is a variable that can take different values according to the outcome of an experiment, and it can be either discrete or continuous. _____14. The variance is the expected value of the squared difference between the random variable and its mean. _____15. If the critical values of the test statistic z is ±1.96, they are the dividing points between the areas of rejection and non-rejection. _____16. For the continuity correction, the normal distribution is continuous and the binomial is discrete. _____17. The binomial probability table gives probability for value of p greater than 0.5. _____18. The cannot be written without having an equal sign. _____19. For the normal distribution, the observations closer to the middle will occur with increasing frequency. _____20. One assumption in testing a hypothesis about a proportion is that an outcome of an experiment can be classified into two mutual categories, namely, a success or a failure.
Part C: Answer the following questions (21-29)
21. Explain the differences between discrete random variable and continuous random variable. 22. What are the characteristics of discrete probability distribution? 23. When should the z-test be used and when should t-test be used? 24. What is the purpose of hypothesis testing? 25. Can you prove the null? Why?
26. What is Type I error? 27. What is Type II error? 28. Explain Sampling distribution of the mean 29. Explain Central limit theorem Part D:Fill in the blank (30-40) 30. The purpose of hypothesis testing is to aid the manager or researcher in reaching a (an) __________________ concerning a (an) _______________ by examining the data contained in a (an) _______________ from that ____________________. 31. A hypothesis may be defined simply as __________________________________________. 32. There are two statistical hypotheses. They are the _________________ hypothesis and the _________________ hypothesis. 33. The statement of what the investigator is trying to conclude is usually placed in the _________________ hypothesis. 34. If the null hypothesis is not rejected, we conclude that the alternative _________________. 35. If the null hypothesis is not rejected, we conclude that the null hypothesis _________________. 36. The probability of committing a Type I error is designated by the symbol ____________, which is also called the ___________________. 37. Values of the test statistic that separate the acceptance region from the rejection are called _________________ values. 38. The following is a general statement of a decision rule: If, when the null hypothesis is true, the probability of obtaining a value of the test statistic as_______________ as or more _____________ than that actually obtained is less than or equal to , the null hypothesis is________________. Otherwise, the null hypothesis is ______________________ . 39. The probability of obtaining a value of the test statistic as extreme as or more extreme than that actually obtained, given that the tested null hypothesis is true, is called ____________ for the ________________test. 40. When one is testing H0: µ= µ0 on the basis of data from a sample of size n from a normally distributed population with a known variance of ?2, the test statistic is ____________________________________________________. Part E:Must show all your work step by step in order to receive the full credit; Excel is not allowed. (41-53)
41. Ten trials are conducted in a Bernoulli process in which the probability of success in a given trail is 0.4. If x = the number of successes, determine the following.
42. Work problem number 5 on page 6-14 (a-e).
43. Work problem number 9 on page 6-28 (a-f).
44. Use problem number 4 on page 6-22 to fill in the table and answer the following questions (a-c).
45. Work problem number 5 on page 7-23 (a-f).(**Please draw the graph)
46. Work problem number 9 on page 7-47 (a-f). (** Please draw the graph)
47. Find the following probabilities:(**Please draw the graph)
48. Find the Z scores for the following normal distribution problems.(** Please draw the graph)
49. Work problem on number 11 (a - f) on page 7-47 (a-f). (** Please draw the graph)
50. Work problem on number 3 on page 8-10. 51. Work problem on number 12 on page 8-11. 52. Consider the following hypothesis test Ho: µ ? 10 Ha: µ < 10 A sample of 50 provides a sample mean of 9.46 and sample variation of 4.
53. Consider the following data drawn from a normal distribution population:
Construct 95% confidence interval using the above information and answer the following questions.
Part C: Answer the following questions (21-29) Part D: Fill in the blank (30-40) Part E: Work Problem (41-53) **All work must be shown step by step** v **Excel is not acceptable for this test v **Deadline:Monday, October 26, 2014 by noon (CST) v **All work in part D must be shown step by step in order to receive credit
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Part A: Multiple Choice (1–10)
____1. The cumulative probability distribution of a random variable X gives the probability that X is _______ to , some spacified value of X.
a. Greater than or equal c. Less than or equal
b. Equal d. None of the above
_____2. The_______is the smallest level of significance at which can be rejected.
a. Value of c. p value
b. Probability of commiting of Type I error d. vale of 1 –
_____3. What is the probability of P(-1.4 < Z < 0.6)?
a. 0.9254 c. 0.3427
b. 0.6449 d. 0.9788
_____4. By using the binomial table, if the sample size is 20 and p equals to 0.70, what is the
value for P(X 18)?
a. 0.0279 c. 0.1820
b. 0.0375 d. 0.1789
_____5. In a standard normal distribution, what is the area which lies between Z = -1.72 and
Z = 2.53?
a. 0.8948 c. 0.9516
b. 0.9123 d. 0.8604
_____6. A random sample of 60 items is taken producing a sample mean of 25 and a sample standard deviation of 12.25. What is the value for 95% confidence interval to estimate the population mean?
a. 23.3844 24.8966 c. 28.3541 29.1359
b. 24.1144 25.8856 d. 25.8252 26.5478
_____7.You perform a hypothesis test about a population mean on the basis of the following information: the sampled population is normally distributed, s = 100, n = 25, = 225, ? = 0.05, Ha: µ > 220. The critical value of the test statistic is ______________ .
a. 2.0639 b. 1.7081
c. 1.7109 d. 1.96
_____8.You perform a hypothesis test about a population mean on the basis of the following information: n = 50, = 100, ? = 0.05, s = 30, Ha: µ < 110. The computed value of the test statistic is _____________ .
a. -2.3570 b. -1.645
c. 2.3570 d. 4.24264
_____9. What is score for P(Z ) = 0.0708?
a. 1.47 c. 1.80
b. 1.35 d. 1.41
_____10. The random variable x has a normal distribution with = 40 and = 36. What is the value of x if P(X ) = 0.40?
a. 47.86 c. 49.85
b. 41.50 d. 45.73
Part B: True or False (11-20)
_____11. A normal distribution is a distribution of discrete data that produces a bell-shaped.
_____12. The mean of the discrete probability distribution for a discrete random variable is called its expected value.
_____13. A random variable is a variable that can take different values according to the outcome of an experiment, and it can be either discrete or continuous.
_____14. The variance is the expected value of the squared difference between the random variable and its mean.
_____15. If the critical values of the test statistic z is ±1.96, they are the dividing points between the areas of rejection and non-rejection.
_____16. For the continuity correction, the normal distribution is continuous and the binomial is discrete.
_____17. The binomial probability table gives probability for value of p greater than 0.5.
_____18. The cannot be written without having an equal sign.
_____19. For the normal distribution, the observations closer to the middle will occur with increasing frequency.
_____20. One assumption in testing a hypothesis about a proportion is that an outcome of an experiment can be classified into two mutual categories, namely, a success or a failure.
Part C: Answer the following questions (21-29)
21. Explain the differences between discrete random variable and continuous random variable.
22. What are the characteristics of discrete probability distribution?
23. When should the z-test be used and when should t-test be used?
24. What is the purpose of hypothesis testing?
25. Can you prove the null? Why?
26. What is Type I error?
27. What is Type II error?
28. Explain Sampling distribution of the mean
29. Explain Central limit theorem
Part D:Fill in the blank (30-40)
30. The purpose of hypothesis testing is to aid the manager or researcher in reaching a (an) __________________ concerning a (an) _______________ by examining the data contained in a (an) _______________ from that ____________________.
31. A hypothesis may be defined simply as __________________________________________.
32. There are two statistical hypotheses. They are the _________________ hypothesis and the _________________ hypothesis.
33. The statement of what the investigator is trying to conclude is usually placed in the _________________ hypothesis.
34. If the null hypothesis is not rejected, we conclude that the alternative _________________.
35. If the null hypothesis is not rejected, we conclude that the null hypothesis _________________.
36. The probability of committing a Type I error is designated by the symbol ____________, which is also called the ___________________.
37. Values of the test statistic that separate the acceptance region from the rejection are called _________________ values.
38. The following is a general statement of a decision rule: If, when the null hypothesis is true, the probability of obtaining a value of the test statistic as_______________ as or more _____________ than that actually obtained is less than or equal to , the null hypothesis is________________. Otherwise, the null hypothesis is ______________________ .
39. The probability of obtaining a value of the test statistic as extreme as or more extreme than that actually obtained, given that the tested null hypothesis is true, is called ____________ for the ________________test.
40. When one is testing H0: µ= µ0 on the basis of data from a sample of size n from a normally distributed population with a known variance of ?2, the test statistic is ____________________________________________________.
Part E:Must show all your work step by step in order to receive the full credit; Excel is not allowed. (41-53)
41. Ten trials are conducted in a Bernoulli process in which the probability of success in a given trail is 0.4. If x = the number of successes, determine the following.
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a) E(x) |
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c) P (x = 5) |
d) P (4 ? x ? 8) |
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e) P (x > 4) |
42. Work problem number 5 on page 6-14 (a-e).
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43. Work problem number 9 on page 6-28 (a-f).
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44. Use problem number 4 on page 6-22 to fill in the table and answer the following questions (a-c).
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(X)(P[X=x]) |
[X-E(X)] |
[X-E(X)]2 |
[X-E(X)]2 P[X=x] |
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Total |
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a) Expected value
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b) Variance |
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c) Standard deviation |
45. Work problem number 5 on page 7-23 (a-f).(**Please draw the graph)
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Show your work |
Please draw graph |
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46. Work problem number 9 on page 7-47 (a-f). (** Please draw the graph)
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Show your work |
Please draw graph |
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47. Find the following probabilities:(**Please draw the graph)
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Show your work |
Please draw graph |
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P(-1.4 < Z < 0.6) |
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P(Z > -1.44) |
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P(Z < 2.03) |
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P(Z > 1.67) |
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P(Z < 2.84) |
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P(1.14 < Z < 2.43) |
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48. Find the Z scores for the following normal distribution problems.(** Please draw the graph)
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Show your work |
Please draw graph |
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µ = 604,? = 56.8, P(X ? 635) |
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µ = 48,?2 = 144, P(X< 20)
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µ = 111,? = 33.8, P(100?X? 150) |
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µ = 264,?2 = 118.81, P(250<X< 255) |
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µ = 37,? = 4.35, P(X > 35) |
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µ = 156,? = 11.4, P(X ? 170) |
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49. Work problem on number 11 (a - f) on page 7-47 (a-f). (** Please draw the graph)
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Show your work |
Please draw graph |
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50. Work problem on number 3 on page 8-10.
51. Work problem on number 12 on page 8-11.
52. Consider the following hypothesis test
Ho: µ ? 10
Ha: µ < 10
A sample of 50 provides a sample mean of 9.46 and sample variation of 4.
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a) Use Z or T test? And why? |
b) At ? = 0.05, what is the rejection rule? |
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c) Compute the value of the test statistic.
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d) What is the p-value? |
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e) What is your conclusion?
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53. Consider the following data drawn from a normal distribution population:
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Construct 95% confidence interval using the above information and answer the following questions.
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a) What is sample mean |
b) What is sample standard deviation |
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c) Use Z or T test? And why? |
d) At At 95% confidence interval, what is the rejection rule? |
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e) Compute the value of the test statistic.
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f) What is associated with this question? |
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g) Interpret the confidence interval
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Solution: Texas Eco578 Exam II 2015