Take Homeexam II

ECO 578 Page 1 of 14

Name: ______

ID: ______

Take HomeExam II

Part A: Multiple Choice (1–13)

____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 equalc. Less than or equal

b.Equald. None of the above

_____2. What is the probability of P(-1.4 < Z < 0.6)?

0.9254c. 0.3427
0.6449d. 0.9788

_____3. By using the binomial table, if the sample size is 20 and p equals to 0.70, what is the

value for P(X18)?

0.0279c. 0.1820
0.0375d. 0.1789

_____4. In a standard normal distribution, what is the area which lies between Z = -1.72 and

Z = 2.53?

a.0.8948c. 0.9516

b.0.9123d. 0.8604

_____5. What is the value for 95% confidence interval for if = 7.3, x = 84.2, and n = 40.

a. 81.93786.463c. 74.09379.337

68.76772.033d. 61.36466.846

_____6. The ______is the smallest level of significance at which H0 can be rejected.

a. value of αc. p value

b. probability of committing of Type I error d. value of 1- α

_____7. We say that sample results are significant when ______.

a. H0 is not rejected

b. H0 is rejected

c. is smaller than the p value

d. the computed value of the test statistic falls in the acceptance region

_____8. We commit a Type 1 error if we ______a true null hypothesis.

a. fail to rejectc. reject

b. acceptd. compute

_____9. Given:H0: µ = 10, Ha: µ ≠ 10, n = 12, α = 0.01, and the computed test statistic is 2.394, the p value for the test is ______.

a.between 0.02 and 0.01b. between 0.025 and 0.01

c.between 0.05 and 0.02d.none of the above

_____10. We say that sample results are significant when ______.

a. H0 is not rejected

b. H0 is rejected

c. is smaller than the p value

d. the computed value of the test statistic falls in the acceptance region

_____11. 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.-2.3570b.-1.645

c.2.3570d.4.24264

_____12. Given: H0: µ ≥ 100, the alternative hypothesis is ______if the test is one-sided and the critical value is negative.

a.µ < 100b.µ > 100

c.µ = 100d.µ ≠220

_____13. You perform a hypothesis test about a population mean on the basis of the following information: The sampled population is normally distributed with a variance of 100, n= 25, = 225, α = 0.05, Ha: µ > 220. The critical value of the test statistic is ______

a.2.5b.1.645

c.1.7109d.1.96

Part B: Fill in the blank Question number (14-24)

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.

A Type I error occurs when the investigator __________________.

Values of the test statistic that separate the acceptance region from the rejection are called _______________values.

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 ____________.

The null hypothesis contains a statement of ________________.

The statement µ ≥ 0 is an inappropriate statement for the ______________hypothesis.

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

Please consider “reject” or “fail to reject” by using one tailed and two-tailed method (Part A&B):

P-Value / A)One-tailed / B)Two-tailed
Computed / Critical / Reject / Fail to Reject / Reject / Fail to Reject
a) / p = 0.12 / α = 0.05
b) / p = 0.03 / α = 0.05
c) / p = 0.001 / α = 0.01
d) / p = 0.01 / α = 0.001

Part C: Answer the following questions (25-28)

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?

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. (29-39)

The random variable X has a normal distribution with mean 50 and variance 9. Find thevalue of X, call it :

a) / / b) /
c) / / d) /

Use problem number 3 on page 6-23 to fill in the table and answer the following questions.

x / Probability / Weighted Value / Deviation / Deviation2 / Weighted Squared Deviation
0
1
2
3
4
5
6
7
Total

Please answer the following questions:

a)Mean / b)Variance / c)Standard Deviation

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

a) / b)
c) / d)
e)

Work on problem number 12 (a-e) on page 6-16

a) / b)
c) / d)
e)

Use the following information to conduct the confidence intervals specified to estimate μ.

95% confidence; =25, = 12.25, and n=60.

98% confidence; =119.6, = 570.7321, and n=25.

Given the following probabilities, find Z0 and please draw the shading the area:

Show your work / Please draw graphs
a. / P /

b. / P /
c. / P /
d. / P /
e. / P
f. / P

Work problem number 9 on page 7-47.

Show your work / Please draw graphs
a. /

b. /
c. /
d. /
e. /
f. /

Find the following probabilities:

Show your work / Please draw graphs
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) /

Work problem number 23 on page 7-25 (a-f) to find Z-score and probability.

Show your work / Please draw graphs
a. /

b. /
c. /
d. /
e. /
f. /

38. Work example 1 on page 7-53 (a-f) (using normal approximation to the binomial distribution)

Binomial / Normal
a.
b.
c.
d.
e.
f.

39. Work problem number 21 on page 7-25 (a-e).

Show your work / Please draw graphs
a. /

b. /
c. /
d. /
e. /