**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**

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.

Essays

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.

Reviews

Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Reviews

Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.