stat exam 2

_____10. 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, H1: µ > 220. The critical value of the test statistic is ______________.

a. 2.0639 c. 1.7081

b. 1.7109 d. 1.96

Part B: Fill in the blank Questions number (11-20)

11. 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 ____________________.

12. A hypothesis may be defined simply as __________________________________________.

13. There are two statistical hypotheses. They are the _________________ hypothesis and the _________________ hypothesis.

14. A Type I error occurs when the investigator _____________________________.

15. Values of the test statistic that separate the acceptance region from the rejection are called _________________ values.

16. 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.

17. 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 ____________________________________________________.

18. The null hypothesis contains a statement of __________________________________.

19. The statement µ ≥ 0 is an inappropriate statement for the ____________ hypothesis.

20. The null hypothesis and the alternative hypothesis are ____________ of each other.

Part C: Answer the following questions (21-24)

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. Explain the following concept:

a. Central Limit Theorem

b. Type I error and Type II error

Part D: Must show all your work step by step in order to receive the full credit; Excel is not allowed. (25-36)

25. Work problem number 5 on page 6-13.

Determine the following probabilities by use of the table of binomial probabilities

a. P(X=1 ǀ n = 10, p = 0.40)

b. P(X = 2 ǀ n=10, p=0.70)

c. P(X ≤ 16 ǀ n = 50, p = 0.50)

d. P(X < 5 ǀ n= 10, p = 0.60)

e. P(X ≥ 8 ǀ n = 50, p = 0.80)

26. Assume that X is a binomial random variable with n = 20, and p = 0.7. Use a binomial approximation to find the following:

a. P(X = 18)

b. P(X = 15)

c. P(X ≤ 20)

d. P(X ≥ 16)

e. P(2 ≤ X ≤ 17)

27. Determine the mean, the variance, and the standard deviation of the following discrete distribution:

x	P(X=x)
0	0.112
1	0.238
2	0.014
3	0.234

28. Ten trials are conducted in a Bernoulli process in which the probability of success in a given trial is 0.4. If x = the number of successes, determine the following.

a. P (x = 5)

b. P (4 ≤ x ≤ 8)

c. P (x > 4)

29. Given the following probabilities, Find Zo: (***Please draw the graph)

a. P(z ≤ Zo) = 0.0055 b. P(Zo ≤ z ≤ 2.98) = 0.1117

c. P(-2.67≤ z ≤ Zo) = 0.9718 d. P(-Zo ≤ z ≤ Zo ) = 0.8132

e. P(z > Zo) = 0.0384 f. P(z ≥ Zo) = 0.06

30. Find the following probabilities: if μ = 160, σ = 16

a.