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Hypotesting Multiple choice and Short Answer Questions

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Question;Name: ________________________ Class: ___________________ Date: __________ ID: A1HypoTestingMultiple ChoiceIdentify the choice that best completes the statement or answers the question.____ 1. A Type II error is committed if we make:a. a correct decision when the null hypothesis is false.b. a correct decision when the null hypothesis is true.c. an incorrect decision when the null hypothesis is false.d. an incorrect decision when the null hypothesis is true.____ 2. The hypothesis of most interest to the researcher is:a. the alternative hypothesis.b. the null hypothesis.c. both hypotheses are of equal interest.d. Neither hypothesis is of interest.____ 3. A Type I error occurs when we:a. reject a false null hypothesis.b. reject a true null hypothesis.c. don't reject a false null hypothesis.d. don't reject a true null hypothesis.____ 4. A Type II error is defined as:a. rejecting a true null hypothesis.b. rejecting a false null hypothesis.c. not rejecting a true null hypothesis.d. not rejecting a false null hypothesis.____ 5. The probability of a Type II error is denoted by:a. ab. bc. 1? ad. 1? b____ 6. Which of the following would be an appropriate alternative hypothesis?a. The mean of a population is equal to 70.b. The mean of a sample is equal to 70.c. The mean of a population is greater than 70.d. The mean of a sample is greater than 70.____ 7. Suppose we wish to test H0:? = 45 vs. H1:? > 45. What will result if we conclude that the mean is greaterthan 45 when the actual mean is 50?a. We have made a Type I error.b. We have made a Type II error.c. We have made both a Type I error and a Type II error.d. We have made the correct decision.____ 8. Researchers claim that 60 tissues is the average number of tissues a person uses during the course of a cold.The company who makes Kleenex brand tissues thinks that fewer of their tissues are needed. What are theirnull and alternative hypotheses?a. H0:? = 60 vs. H1:? > 60b. H0:? = 60 vs. H1:? < 60c. H0: X = 60 vs. H1: X < 60d. H0:? 100, the p-value is found to be 0.074, and the sample meanis 105. Which of the following statements is true?a. The probability of observing a sample mean at least as large as 105 from a populationwhose mean is 100 is 0.074.b. The probability of observing a sample mean smaller than 105 from a population whosemean is 100 is 0.074.c. The probability that the population mean is larger than 100 is 0.074.d. None of these choices.____ 14. The p-value of a test is the:a. smallest a at which the null hypothesis can be rejected.b. largest a at which the null hypothesis can be rejected.c. smallest a at which the null hypothesis cannot be rejected.d. largest a at which the null hypothesis cannot be rejected.____ 15. We have created a 95% confidence interval for? with the results (10, 25). What conclusion will we make ifwe test H0:? = 26 vs. H1:? ? 26 at a = 0.025?a. Reject H0 in favor of H1b. Accept H0 in favor of H1c. Fail to reject H0 in favor of H1d. We cannot tell from the information given.____ 16. The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club. Shewould now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alterthe entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose shefound that the sample mean was 35.5 years and the population standard deviation was 5 years. What is thep-value associated with the test statistic?a. 0.9582b. 1.7300c. 0.0418d. 0.0836____ 17. The numerical quantity computed from the data that is used in deciding whether to reject H0 is the:a. significance level.b. critical value.c. test statistic.d. parameter.____ 18. The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club. Shewould now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alterthe entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants tobe 99% confident in her decision, what rejection region she use if the population standard deviation s isknown?a. Reject H0 if z 2.58____ 19. For a given level of significance, if the sample size increases, the probability of a Type II error will:a. remain the same.b. increase.c. decrease.d. be equal to 1.0 regardless of a.____ 20. The power of a test is measured by its capability of:a. rejecting a null hypothesis that is true.b. not rejecting a null hypothesis that is true.c. rejecting a null hypothesis that is false.d. not rejecting a null hypothesis that is false.____ 21. If the probability of committing a Type I error for a given test is decreased, then for a fixed sample size n, theprobability of committing a Type II error will:a. decrease.b. increase.c. stay the same.d. Not enough information to tell.____ 22. The power of a test is denoted by:a. ab. bc. 1? ad. 1? b____ 23. For a given level of significance a, if the sample size n is increased, the probability of a Type II error b will:a. decrease.b. increase.c. remain the same.d. Not enough information to tell.____ 24. For statistical inference about the mean of a single population when the population standard deviation isunknown, the degrees for freedom for the t-distribution equal n? 1 because we lose one degree of freedomby using the:a. sample mean as an estimate of the population mean.b. sample standard deviation as an estimate of the population standard deviation.c. sample proportion as an estimate of the population proportion.d. sample size as an estimate of the population size.____ 25. A major department store chain is interested in estimating the average amount its credit card customers spenton their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampledand analyzed with the following results: x = $50.50 and s2 = 400. A 95% confidence interval for the averageamount the credit card customers spent on their first visit to the chain's new store in the mall is:a. $50.50 ? $9.09.b. $50.50 ? $10.12.c. $50.50 ? $11.08.d. None of these choices.____ 26. Under what condition(s) does the test statistic for p have an approximate normal distribution?a. When np > 5.b. When np and np(1? p) are both > 5.c. When n > 30.d. When np and n(1? p) are both > 5.____ 27. After calculating the sample size needed to estimate a population proportion to within 0.04, your statisticsprofessor told you the maximum allowable error must be reduced to just.01. If the original calculation led toa sample size of 800, the sample size will now have to be:a. 800b. 3200c. 12,800d. 6400____ 28. The width of a confidence interval estimate for a proportion will be:a. narrower for 99% confidence than for 95% confidence.b. wider for a sample size of 100 than for a sample size of 50.c. narrower for 90% confidence than for 95% confidence.d. narrower when the sample proportion if 0.50 than when the sample proportion is 0.20.True/FalseIndicate whether the statement is true or false.____ 29. There is an inverse relationship between the probabilities of Type I and Type II errors, as one increases, theother decreases, and vice versa.____ 30. For a given level of significance, if the sample size is increased, the probability of committing a Type II errorwill decrease.____ 31. The critical values will bound the rejection and non-rejection regions for the null hypothesis.____ 32. A one-tail test for the population mean? produces a test-statistic z =?0.75. The p-value associated with thetest is 0.7734.____ 33. For a given level of significance, if the sample size is increased, the probability of committing a Type I errorwill decrease.____ 34. The power of the test refers to the probability of rejecting a false null hypothesis.____ 35. As the alternative value of? increases, so does the power of the test.____ 36. The statistic (x??) / (s / n) when the sampled population is normal is Student t-distributed with n degreesof freedom.____ 37. The lower limit of the 90% confidence interval for the population proportion p, given that n = 400 and p8 =0.10, is 0.0247.____ 38. In determining the sample size needed to estimate the population proportion p, we let the sample proportion p8= 1 if we have no knowledge of even the approximate values of p8.Short Answer39. Suppose a delivery company states that their packages arrive within two days or less on average. You want tofind out whether the actual average delivery time is longer than this. You conduct a hypothesis test.a. Set up the null and alternative hypotheses.b. Suppose you conclude wrongly that the company's statement about average delivery timeis within two days. What type of error is being committed and what is the impact of thaterror?c. Suppose you conclude wrongly that the delivery company's average time to delivery is infact longer than two days. What type of error did you commit and what is the impact ofthis error?d. Which error is worse from the company's standpoint, a Type I or a Type II error? Why?e. Which error is worse from a consumer standpoint, a Type I or a Type II error? Why?GRE ScoresThe Admissions officer for the graduate programs at Michigan State University (MSU) believes that theaverage score on the GRE exam at his university is significantly higher than the national average of 1,300.An accepted standard deviation for GRE scores is 125. A random sample of 25 scores had an average of1,375.40. {GRE Scores Narrative} Calculate the value of the test statistic and set up the rejection region at the 0.025level. What is your conclusion?41. {GRE Scores Narrative} Calculate the p-value.Grocery ReceiptsA simple random sample of 100 grocery receipts was drawn from a normal population. The mean andstandard deviation of the sample were $120 and $25, respectively.42. {Grocery Receipts Narrative} Test the hypothesis H0:? = 125 vs. H1:? ? 125 at the 10% significance level.43. A drug company has just developed a new pill to alleviate the symptoms of allergies and colds. However,they are concerned about the variability in the amount of time until the drug becomes effective. In a randomsample of 10 individuals who suffer from allergies, the amount of time (in hours) for the pill to take effectwas recorded and listed as follows: 5, 7, 6, 10, 9, 12, 8, 17, 4, and 16. Estimate with 90% confidence thevariance of the time for the drug to become effective.Independent VotersA pollster wants to challenge a claim that 5% of the registered voters in her state are Independent, she thinksthe percentage is lower than that. In a test of hypothesis, H0: p = 0.05 vs. H1: p < 0.05, her random sample ofsize 1,000 registered voters revealed that the number of Independents was 40.44. {Independent Voters Narrative} Compute the p-value and explain how to use it to test the hypotheses.Union ContractA union composed of several thousand employees is preparing to vote on a new contract. A random sampleof 500 employees yielded 320 who planned to vote yes. It is believed that the new contract will receive morethan 60% yes votes.45. {Union Contract Narrative} Compute the p-value for the test.New ProductAfter a financial analysis, the general manager of a large company decided that if more than 8% of potentialbuyers of a new product purchase that product, the company would show a profit. In a preliminary survey of500 potential buyers, 56 people say that they will buy the product.46. {New Product Narrative} Is there sufficient evidence at the 5% significance level that the product willproduce a profit?Allergy DrugA company claims that 10% of the users of a certain allergy drug experience drowsiness. In clinical studiesof this allergy drug, 81 of the 900 subjects experienced drowsiness47. {Allergy Drug Narrative} Is there enough evidence at the 5% significance level to infer that the competitor iscorrect?Car DealershipAn accountant was performing an audit for a car dealership. An auditor wants to examine the monetary errormade by the purchasing order department in the month of July. He decided to randomly sample 100 of the925 purchase orders for the month of July, and found the amount of error in each one. The statistics for thissample were: x = $6.0 and s = $17.012.48. {Car Dealership Narrative} Estimate with 95% confidence the average amount of error per purchase orderfor the entire month of July.

 

Paper#62102 | Written in 18-Jul-2015

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