STAT FINAL EXAM

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1. If n=15 and p=0.4, then the standard deviation of the binomial distribution is 3.6. (Ch6)(Points : 8)

        True          False 

Question 2.2. If the level of confidence and sample size remain the same, a confidence interval for a population proportion p will be narrower when p(1-p) is larger than when it is smaller. (Ch9) (Points : 8)

        True          False 

Question 3.3. In a simple linear regression model, the coefficient of determination not only indicates the strength of the relationship between independent and dependent variable, but also shows whether the relationship is positive or negative. (Ch13) (Points : 8)

        True          False 

Question 4.4. The sample standard deviation s is an unbiased estimator of the population standard deviation. (Ch8)  (Points : 8)

        True          False 

Question 5.5. If the random variable of x is normally distributed, 68.26% of all possible observed values of x will be within two standard deviations of the mean. (Ch7) (Points : 8)

        True          False 

Question 6.6. If n=20 and p=.4, then the mean of the binomial distribution is 8 (Ch6) (Points : 8)

        True          False 

Question 7.7. First a confidence interval is constructed without using the finite population correction factor. Then, for the same identical data, a confidence interval is constructed using the finite population correction factor. The width of the interval with the finite population correction factor is wider than the confidence interval without the finite population correction factor. (Ch9) (Points : 8)

        True          False 

Question 8.8. The power of a statistical test is the probability of rejecting the null hypothesis when it is true. (Ch10) (Points : 8)

        True          False 

Question 9.9. The sampling distribution of the sample mean is developed by repeatedly taking samples of size n and computing the sample means and reporting the resulting sample means in the form of a probability distribution. (Ch8) (Points : 8)

        True          False 

Question 10.10. For a continuous distribution, the exact probability of a particular value is always zero. (Ch7) (Points : 8)

        True          False 

Question 11.11. As the level of significance  increases, we are more likely to reject the null hypothesis. (Ch10) (Points : 8)

        True          False 

Question 12.12. If events A and B are mutually exclusive, then P(A|B) is always equal to zero. (Ch5) (Points : 8)

        True          False 

Question 13.13. If p=.9 and n=40, then we can conclude that the sampling distribution of  the proportions is approximately a normal distribution. (Ch8) (Points : 8)

        True          False 

Question 14.14. The standard deviation of the sampling distribution of the sample mean is the same as the population standard deviation. (Ch8) (Points : 8)

        True          False 

Question 15.15. If events A and B are mutually exclusive, then P(A and B) is always equal to zero. (Ch5) (Points : 8)

        True          False 

Question 16.16. If a null hypothesis is rejected at a significance level of .01, it will ______ be rejected at a significance level of .05 (Ch10) (Points : 12)

        Always         Sometimes         Never

Question 17.17. The internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent more than 90 days overdue. The historical records of the company show that over the past 8 years 14 percent of the accounts are delinquent. For this quarter, the auditing staff randomly selected 250 customer accounts. What is the probability that at least 30 accounts will be classified as delinquent? (Ch8) (Points : 12)

        31.86%         18.14%         81.86%         63.72%         75.84%

Question 18.18. The price-to-earning ratio for firms in a given industry is distributed according to normal distribution. In this industry, a firm with a standard normal variable value of Z=1: (Ch7) (Points : 12)

        Has an above average price-to-earning ratio         Has an below average price-to-earning ratio         Has an average price-to-earning ratio         May have an average or below average price-to-earnings ratio

Question 19.19. In a manufacturing process a random sample of 9 bolts manufactured has a mean length of 3 inches with a standard deviation of .3 inches. What is the 95% confidence interval for the true mean length of the bolt? (Ch9) (Points : 12)

        2.904 to 3.396         2.308 to 3.692         2.412 to 3.588         2.770 to 3.231         2.884 to 3.086

Question 20.20. The point estimate of the variance in a regression model is (Ch13) (Points : 12)

        SSE         β(0)         β(1)         MSE

Question 21.21. The mean life of pair of shoes is 40 months with a standard deviation of 8 months. If the life of the shoes is normally distributed, how many pairs of shoes out of one million will need replacement before 36 months? (Ch7) (Points : 12)

        500,000         808,500         191,500         308,500

Question 22.22. When determining the sample size, if the value found is not an integer initially, the next highest integer value will ____________ be chosen. (Ch9) (Points : 12)

        Always         Sometimes         Never

Question 23.23. The _______ of two events X and Y is another event that consists of the sample space outcomes belonging to  both event X and Y. (Ch5) (Points : 12)

        Sample space outcome         Conditional Probability         Complement of events         Long-run relative frequency         Intersection

Question 24.24. A multiple-choice test has 30 questions and each one has five possible answers, of which one is correct. If all answers were guesses, find the probability of getting exactly four correct answers. (Ch6) (Points : 12)

        0.0604         0.1325         0.2552         0.8000

Question 25.25.  (Points : 12)

        H0 is rejected         H0 is not rejected         H0 may or may not be rejected depending on the sample size n         Additional information is needed and no conclusion can be reached about whether H0should be rejected

Question 26.26. A standard normal distribution has a mean of _____ and standard deviation of _____.   (Ch7) (Points : 12)

        Zero, Zero         Zero, One         One, One         One, Zero

Question 27.27. The average customer waiting time at a fast food restaurant has been 7.5 minutes. The customer waiting time has a normal distribution. The manager claims that the use of a new system will decrease average customer waiting time in the store. What is the null and alternative hypothesis for this scenario? (Ch10) (Points : 12)

        H0: =7.5 and HA: ≠ 7.5         H0: ≤ 7.5 and HA:  > 7.5         H0: ≥ 7.5 and HA:  < 7.5         H0: <7.5 and HA: ≥ 7.5         H0: > 7.5 and HA:  ≤ 7.5

Question 28.28. If the wages of workers for a given company are normally distributed with a mean of $15 per hour, then the proportion of the workers earning more than $13 per hour: (Ch7) (Points : 12)

        Is less than the proportion earning less than $13 per hour         Is equal to the proportion earning less than $13 per hour         Is greater than the proportion earning less than $13 per hour         Is less than 50%         Cannot tell from the information given.

Question 29.29. In a study conducted by UCLA, it was found that 25% of college freshmen support increased military spending. If 6 college freshmen are randomly selected, find the probability that:  “fewer than 4 support increased military spending” (Ch6) (Points : 12)

        0.9624         0.9954         0.7844         0.0330

Question 30.30. When the level of confidence and the sample size remain the same, a confidence interval for a population mean µ will be ________________, when the sample standard deviation s is smaller than when s is larger.  (Ch9) (Points : 12)

        Wider         Narrower         Sometimes wider, sometimes narrower.         They will be the same

Question 31.31. Container 1 has 8 items, 3 of which are defective. Container 2 has 5 items, 2 of which are defective. One item is drawn from each container: What is the probability that one of the items is defective? (Hint: you have to use both rule of addition and rule of multiplication/conditional probability rules) (Ch5) (Points : 25)

             

Question 32.32. Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25% for University A and 40% for University B. What is the probability that Joe will be accepted at one and only one university? (Ch5) (Points : 25)

             

Question 33.33. The probability that an appliance is in repair is .5. If an apartment complex has 100 such appliances, what is the probability that at least 60 will be in repair? Use the normal approximation to the binomial. (Ch7) (Points : 25)

             

Question 34.34. The J.O. Supplies Company buys calculators from a Korean supplier. The probability of a defective calculator is 10%. If 100 calculators are selected at random, what is the standard deviation of the number of defectives? (Ch6) (Points : 25)

             

Question 35.35. A random sample of size 36 from a normal population yields  mean X-bar = 32.8 and standard deviation s = 4.51. Construct a 95 percent confidence interval for μ. (Ch9) (Points : 25)

             

Question 36.36. Employees of a local university have been classified according to gender and type of job as follows: Job                       Male         Female  Faculty                    110            10  Salaried staff             30             50 Hourly staff               60            40 If an employee is selected at random, what is the probability that the employee is a female or works as an hourly staff?  (Ch5) (Points : 25)

             

Question 37.37. A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has been frequently failing and requiring repairs and service. The company has been able to provide its customers with a completion time of 6 days or less. To analyze whether the completion time has increased, the production manager took a sample of 25 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days. At a significance level of .05, test whether the completion time has increased.  (form the hypotheses, show the critical and calculated values of the test statistic and perform the test)  (Ch10) (Points : 25)

             

Question 38.38. An important part of the customer service responsibilities of a cable company relates to the speed with which trouble in service can be repaired. Historically, the data show that the likelihood is 0.75 that troubles in a residential service can be repaired on the same day. For the first five troubles reported on a given day, what is the probability that: Fewer than two troubles will be repaired on the same day? (Ch6)