Eco 578 exam ii | Economics homework help
nline Exam II
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.
Greater than or equal c. Less than or equal
Equal d. None of the above
_____2. The_______is the smallest level of significance at which H_o can be rejected.
Value of α c. p value
Probability of commiting of Type I error d. vale of 1 – α
_____3. What is the probability of P(-1.4 < Z < 0.6)?
0.9254 c. 0.3427
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)?
0.0279 c. 0.1820
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?
0.8948 c. 0.9516
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?
23.3844≤μ≤24.8966 c. 28.3541≤μ≤29.1359
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?
1.47 c. 1.80
1.35 d. 1.41
_____10. The random variable x has a normal distribution with μ = 40 and σ^2 = 36. What is the 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)
_____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.
Part C: Answer the following questions (21-29)
Explain the differences between discrete random variable and continuous random variable.
What are the characteristics of discrete probability distribution?
When should the z-test be used and when should t-test be used?
What is the purpose of hypothesis testing?
Can you prove the null? Why?
What is Type I error?
What is Type II error?
Explain Sampling distribution of the mean
Explain Central limit theorem
Part D: Fill in the blank (30-40)
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 ____________________.
A hypothesis may be defined simply as __________________________________________.
There are two statistical hypotheses. They are the _________________ hypothesis and the _________________ hypothesis.
The statement of what the investigator is trying to conclude is usually placed in the _________________ hypothesis.
If the null hypothesis is not rejected, we conclude that the alternative _________________.
If the null hypothesis is not rejected, we conclude that the null hypothesis _________________.
The probability of committing a Type I error is designated by the symbol ____________, which is also called the ___________________.
Values of the test statistic that separate the acceptance region from the rejection are called _________________ values.
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 ______________________ .
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.
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)
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) σ_x
c) P (x = 5)
d) P (4 ≤ x ≤ 8)
e) P (x > 4)
Work problem number 5 on page 6-14 (a-e).
a)
Work problem number 9 on page 6-28 (a-f).
a)
b)
c)
d)
e)
f)
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
Work problem number 5 on page 7-23 (a-f).(**Please draw the graph)
Show your work Please draw graph
Work problem number 9 on page 7-47 (a-f). (** Please draw the graph)
Find the following probabilities:(**Please draw the graph)
Show your work Please draw 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)
Find the Z scores for the following normal distribution problems.(** Please draw the graph)
Show your work Please draw 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)
Work problem on number 11 (a – f) on page 7-47 (a-f). (** Please draw the graph)
Show your work Please draw graph
a.
Ho: µ ≥ 10
Ha: µ < 10
A sample of 50 provides a sample mean of 9.46 and sample variation of 4.
Use Z or T test? And why? At α = 0.05, what is the rejection rule?
Compute the value of the test statistic.
What is the p-value?
What is your conclusion?
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.
What is sample mean What is sample standard deviation
Use Z or T test? And why? At At 95% confidence interval, what is the rejection rule?
Compute the value of the test statistic.
What is α associated with this question?
Interpret the confidence interval
