# BA 578

v  There are 4 parts:

Part A: Select the correct answer for the following questions (1-10)

Part B: True/ False (11-20)

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

Part A : Multiple Choice (1–10)

____1. The cumulative probability distribution of a random variable X gives the probabilitythat 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 samplestandard 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, α  = 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, α = 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 σ2, 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.

a) E(x)

b)

c) P (x = 5)

d) P (4 ≤ x ≤ 8)

e) P (x > 4)

42.  Work problem number 5 on page 6-14 (a-e). a)

b) c)

d) e)

43.  Work problem number 9 on page 6-28 (a-f). a)

b) c)

d) e)

f)

44.  Use problem number 4 on page 6-22 to fill in the table and answer the following questions (a-c).

X

P[X=x]

(X)(P[X=x])

[X-E(X)]

[X-E(X)]2

[X-E(X)]2 P[X=x]

0

1

2

3

4

5

6

Total

a) Expected value

b) Variance c) Standard deviation

45.  Work problem number 5 on page 7-23 (a-f).(**Please draw the graph)

a.

b.

c.

d.

e.

f.

46.  Work problem number 9 on page 7-47 (a-f). (** Please draw the graph)

a. a)

b.

c.

d.

e.

f.

47.  Find the following probabilities:(**Please draw the graph)

a. P(-1.4 < Z < 0.6)

b. P(Z > -1.44)

c. P(Z < 2.03)

d. P(Z > 1.67)

e. P(Z < 2.84)

f. P(1.14 < Z < 2.43)

48.  Find the Z scores for the following normal distribution problems.(** Please draw the graph)

a. µ = 604, σ = 56.8, P(X ≤ 635)

b. µ = 48, σ2 = 144, P(X < 20)

c. µ = 111, σ = 33.8, P(100 ≤ X ≤ 150)

d. µ = 264, σ2 = 118.81, P(250 < X < 255)

e. µ = 37, σ = 4.35, P(X > 35)

f. µ = 156, σ = 11.4, P(X ≥ 170)

49.  Work problem on number 11 (a – f) on page 7-47 (a-f). (** Please draw the graph)

a.

b.

c.

d.

e.

f.

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.

a)      Use Z or T test? And why?

b)      At α = 0.05, what is the rejection rule? c)      Compute the value of the test statistic.

d)      What is the p-value?

e)      What is your conclusion?

53.  Consider the following data drawn from a normal distribution population:

4

8

12

11

14

6

12

8

9

5

Construct 95% confidence interval using the above information and answer the following questions.

a)      What is sample mean

b)      What is sample standard deviation

c)      Use Z or T test? And why? d)      At At 95% confidence interval, what is the rejection rule?

e)      Compute the value of the test statistic.

f)       What is  associated with this question?

g)      Interpret the confidence interval