**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.**

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** What are the characteristics of discrete probability distribution?**

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** When should the z-test be used and when should t-test be used?**

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** What is the purpose of hypothesis testing?**

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** Can you prove the null? Why?**

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** What is Type I error?**

** What is Type II error?**** Explain Sampling distribution of the mean**

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** 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) **

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** b) σ_x**

**c) P (x = 5)**

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** d) P (4 ≤ x ≤ 8)**

**e) P (x > 4)**

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

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

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** b)****c)**

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** d)****e)**

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** 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 **** **

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** b) Variance****c) Standard deviation**

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** 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)**

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** 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) **

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**d. P(Z > 1.67)**

**e. P(Z < 2.84)**

**f. P(1.14 < Z < 2.43)**

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** 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)**

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**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)**** **

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** 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?**

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** 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**

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