Question details

ECO 578 final exams A+
$ 20.00

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**
**Excel is not acceptable for this test
**Deadline: Monday, October 26, 2014 by noon (CST)
**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 probability that X is
_______ to x 0 , 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 H o can be rejected.
a. Value of α
c. p value
b. Probability of commiting of Type I error
d. vale of 1 – α
_____3. What is the probability of P(-1.4 < Z < 0.6)?
a. 0.9254
b. 0.6449

c. 0.3427
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

Page 2 of 16
_____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 ≤ μ ≤ 24.8966
c. 28.3541 ≤ μ ≤ 29.1359
b. 24.1144 ≤ μ ≤ 25.8856
d. 25.8252 ≤ μ ≤ 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, X = 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, X = 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

Z 0 score for P(Z ≥ Z 0 ) = 0.0708?
a. 1.47
b. 1.35

c. 1.80
d. 1.41

_____10. The random variable x has a normal distribution with μ = 40 and
value of x if P(X ≥ X 0 ) = 0.40?
a. 47.86
c. 49.85
b. 41.50
d. 45.73

Part B: True or False (11-20)

σ 2 = 36. What is the

_____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 H o 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.

Page 3 of 16

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

Page 4 of 16

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 ______________________ .

ECO 578 Fall 2015

Page 5 of 16

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.

ECO 578 Fall 2015

Page 6 of 16

42.a) E(x)
43.
44.
45.
46.
47.
48.

49.b) σ x
50.

51.c) P (x = 5)
52.
53.
54.
55.
56.

57.d) P (4 ≤ x ≤ 8)
58.

59.e) P (x > 4)
60.
61.
62.
63.
64.
65.

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

66. a)

77.b)

67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
78.c)
79.
80.

85.d)

ECO 578 Fall 2015

Page 7 of 16

81.
82.
83.
84.
86.e)
87.
88.
89.
90.
91.
92.
93.

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

94. a)
95.
96.
97.
98.
99.
100.
101.
103. c)
104.
105.
106.
107.
108.
109.
111. e)
112.
113.
114.
115.
116.
117.

102. b)

110. d)

118. f)

ECO 578 Fall 2015

Page 8 of 16

119.
120. Use problem number 4 on page 6-22 to fill in the table and answer the following questions
(a-c).
122.

P[X=x]

123. (X)
(P[X=x])

[X-E(X)]

[XE(X)]2

126.

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

X

127.

0

128.

129.

130.

131.

132.

133.

1

134.

135.

136.

137.

138.

139.

2

140.

141.

142.

143.

144.

145.

3

146.

147.

148.

149.

150.

151.

4

152.

153.

154.

155.

156.

157.

5

158.

159.

160.

161.

162.

163.

6

164.

165.

166.

167.

168.

169.

To
tal

170.

171.

172.

173.

174.

175.
176. a) Expected value

124.

125.

121.

185. b) Variance

177.
178.
179.
180.
181.
182.
183.
184.
186. c) Standard deviation
187.
188.
189.
190.
191. Work problem number 5 on page 7-23 (a-f).(**Please draw the graph)
192.
193.
194. Show your work
195. Please draw graph

ECO 578 Fall 2015

196.197.
a.

205.206.
b.

Page 9 of 16

198.
199.
200.
201.
202.
203.
204.
207.

208. 209.
c. 210.

211.

212.213.
d. 214.

215.
216.
217.
218.
219.
220.
221.
224.
225.
226.
227.
228.
229.
230.
233.
234.
235.
236.
237.
238.

222.223.
e.

231.232.
f.

ECO 578 Fall 2015

Page 10 of 16

239.

240. Work problem number 9 on page 7-47 (a-f). (** Please draw the graph)
241.
242.
243. Show your work
244. Please draw graph
245. 246.
a)
248.
a. 247.
249.
250.
251.
252.
253.
254.
255.256.
257.
b.

258. 259.
c. 260.

261.

262.263.
d. 264.

265.
266.
267.
268.
269.
270.
271.

ECO 578 Fall 2015

272.273.
e.

281.282.
f.

Page 11 of 16

274.
275.
276.
277.
278.
279.
280.
283.
284.
285.
286.
287.
288.
289.

290. Find the following probabilities:(**Please draw the graph)
291.
292. Show your work
294.295. P(-1.4 < Z < 0.6)
a. 296.

304.305. P(Z > -1.44)
b. 306.

308.309. P(Z < 2.03)
c.
310.
311.

293. Please draw graph
297.
298.
299.
300.
301.
302.
303.
307.

312.

ECO 578 Fall 2015

313.314. P(Z > 1.67)
d. 315.
316.

324.325. P(Z < 2.84)
e. 326.
327.
328.
329.
337.338. P(1.14 < Z < 2.43)
f. 339.
340.

Page 12 of 16

317.
318.
319.
320.
321.
322.
323.
330.
331.
332.
333.
334.
335.
336.
341.
342.
343.
344.
345.
346.
347.

348. Find the Z scores for the following normal distribution problems.(** Please draw the graph)
349.
350. Show your work
352.353. µ = 604, σ = 56.8, P(X ≤ 635)
a. 354.
355.

363.364. µ = 48, σ2 = 144, P(X < 20)
b. 365.
366.
367.
368.

351. Please draw graph
356.
357.
358.
359.
360.
361.
362.
369.

ECO 578 Fall 2015

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

150)

Page 13 of 16

373.

372.

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

< 255)

376.

384.385. µ = 37, σ = 4.35, P(X > 35)
e. 386.

394.395. µ = 156, σ = 11.4, P(X ≥ 170)
f. 396.

377.
378.
379.
380.
381.
382.
383.
387.
388.
389.
390.
391.
392.
393.
397.
398.
399.
400.
401.
402.
403.

404. Work problem on number 11 (a - f) on page 7-47 (a-f). (** Please draw the graph)
405.
406. Show your work
407. Please draw graph
408.409.
410.
a.
411.
412.
413.
414.
415.
416.

ECO 578 Fall 2015

Page 14 of 16

417.418.

419.

420. 421.
c. 422.

423.

424.425.
d. 426.

427.
428.
429.
430.
431.
432.
433.
436.
437.
438.
439.
440.
441.
442.
445.
446.
447.
448.
449.
450.
451.

b.

434.435.
e.

443.444.
f.

452.
453. Work problem on number 3 on page 8-10.
454.
455.
456.

ECO 578 Fall 2015

Page 15 of 16

457.
458.
459.
460. Work problem on number 12 on page 8-11.
461.
462.
463.
464.
465.
466.
467. Consider the following hypothesis test
468. Ho: µ ≥ 10
469. Ha: µ < 10
470. 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?

471.

473.

472.
e) What is your conclusion?

474.
475.
476.
477. Consider the following data drawn from a normal distribution population:
478.
479. 480. 481. 482. 483. 484. 485. 486. 487. 488.
4

8

12

11

14

6

12

8

9

5

ECO 578 Fall 2015

Page 16 of 16

489.

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

490.
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?

491.

e) Compute the value of the test statistic.

492.
493.

f) What is α

495.

494.
g) Interpret the confidence interval

496.
497.
498.
499.

associated with this question?

 

Available solutions