1 - UC Davis Department of Statistics



|1 |

|The discharge of suspended solids from a phosphate mine is normally distributed, with a mean daily discharge of 27 milligrams per liter (mg/l) |

|and a standard deviation of 14 mg/l. What proportion of days will the daily discharge exceed 50 mg/l? |

|_________ |

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|2 |

|A used-car dealership has found that the length of time before a major repair is required on the cars it sells is normally distributed, with a |

|mean equal to 10 months and a standard deviation of 3 months. If the dealer wants only 5% of the cars to fail before the end of the guarantee |

|period, for how many months should the cars be guaranteed? |

|_________ months |

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|3 |

|Due to a variation in laboratory techniques, impurities in materials, and other unknown factors, the results of an experiment in a chemistry |

|laboratory will not always yield the same numerical answer. In an electrolysis experiment, a class measured the amount of copper precipitated |

|from a saturated solution of copper sulfate over a 30-minute period. The n = 30 students calculated a sample mean and standard deviation equal |

|to 0.145 and 0.0051 mole, respectively. Find a 90% confidence interval for the mean amount of copper precipitated from the solution over a |

|30-minute period. |

|_________ |

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|4 |

|Assume a two-tailed test with z = 3.01 and [pic] = 0.05. Complete the following: |

|p-value: _________ |

|Conclusion: _________________ |

|Assume an upper one-tailed test with z = 2.47 and [pic] = 0.05. Complete the following: |

|p-value: _________ |

|Conclusion: _________________ |

|Assume a two-tailed test with z = -1.30 and [pic] = 0.01. Complete the following: |

|p-value: _________ |

|Conclusion: _________________ |

|Assume a lower one-tailed test with z = -2.88 and [pic] = 0.01. Complete the following: |

|p-value: _________ |

|Conclusion: _________________ |

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|5 |

|The braking ability was compared for two 2005 automobile models. Random samples of 64 automobiles were tested for each type. The recorded |

|measurement was the distance (in feet) required to stop when the brakes were applied at 40 miles per hour. These are the computed sample means |

|and variances: |

|[pic] |

|Do the data provide sufficient evidence to indicate a difference between the mean stopping distances for the two models? |

|Test statistic = _________ |

|p-value = _________ |

|Conclusion: _________________ |

|Interpretation: _________________ |

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|6 |

|The variability in a scientist’s measuring equipment was observed for a random sample of 26 test runs from a normal distribution. The sample |

|yielded a variance of 33. Estimate the population variance using a 95% confidence interval. (use a separate sheet to answer if necessary) |

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|7 |

|Two soft drink machines dispense liquids of 10 ounces, on the average. The question is whether the two machines are equally consistent (i.e., |

|equally variable) in the dispensing of the liquid. To answer this question, a sample of size 10 was obtained from each machine and the sample |

|standard deviations were computed to be [pic] = 1.87 ounces and [pic] = 1.25 ounces. Perform the appropriate test for equality of variances |

|using [pic] = 0.05. (use a separate sheet to answer if necessary) |

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|8 |

|Set up the rejection regions for the following testing conditions. Assume the assumptions of normality and equal variances are satisfied. |

|[pic][pic][pic][pic] |

|[pic] = 10, [pic] = 12, and [pic] = 0.05. |

|[pic][pic][pic][pic] |

|[pic] = 4, [pic] = 8, and [pic] = 0.01. |

|[pic][pic][pic][pic] |

|[pic] = 15, [pic] = 15, and [pic] = 0.05. |

|(use a separate sheet to answer if necessary) |

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|9 |

|An experiment was conducted to study the relationship between the ratings of a tobacco leaf grader and the moisture content of the tobacco |

|leaves. Twelve leaves were rated by the grader on a scale of 1 to 10, and corresponding readings of moisture content were made. |

|[pic] |

|Calculate rs. Do the data provide sufficient evidence to indicate an association between the grader’s ratings and the moisture contents of the |

|leaves? |

|Test statistic = _________ |

|Critical Value(s) = _________ |

|Conclusion: _________________ |

|Interpretation: _________________ |

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|10 |

|A university investigation was conducted to determine whether women and men complete medical school in significantly different amounts of time,|

|on the average. Two independent random samples were selected and the following summary information concerning times to completion of medical |

|school computed: |

|Women Men |

|Sample Size 90 100 |

|Sample Mean 8.4 years 8.5 years |

|Sample Standard Deviation 0.6 years 0.5 years |

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|Perform the appropriate test of hypothesis to determine whether there is a significant difference in time to completion of medical school |

|between women and men. Test using [pic][pic]. |

|Find the p-value associated with the test in part (a). |

|(use a separate sheet to answer if necessary) |

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|11 |

|The Environmental Protection Agency wanted to compare the proportion of plants in violation of air quality standards for two different |

|industries: steel and utility. Two independent samples of plants were selected and monitored. The following data was recorded: |

|Steel: n1 = 150 Number of violations = x1 = 12 |

|Utility: n2 = 160 Number of violations = x2 = 12 |

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|Set up the appropriate null and alternative hypotheses. |

|Compute the value of the test statistic. |

|Set up the appropriate rejection region for a = 0.01. |

|What is the appropriate conclusion? |

|(use a separate sheet to answer if necessary) |

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|12 |

|Let m denote the true average delivery time of a letter from a specific carrier. For a large-sample z test of [pic] : m = 3 versus [pic]m  ¹|

|3, find the p-value associated with each of the given values of the test statistic, and state whether each p-value will lead to a rejection of |

|the null hypothesis when performing a level 0.05 test. |

|[pic][pic] |

|[pic][pic] |

|[pic][pic][pic] |

|[pic][pic] |

|[pic][pic][pic] |

|(use a separate sheet to answer if necessary) |

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|13 |

|A random sample of 150 observations was selected from a binomial population, and 87 successes were observed. Do the data provide sufficient |

|evidence to indicate that the population proportion p is greater than 0.5? Use the critical value approach and the p-value approach. (use a |

|separate sheet to answer if necessary) |

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|14 |

|Suppose that a t-test is being conducted at the 0.05 level of significance to test [pic][pic] versus [pic] . A sample of size 20 is randomly |

|selected. The rejection region is: |

|a. |

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|t > 1.725 |

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|b. |

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|t < -1.729 |

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|c. |

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|t > -2.093 |

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|d. |

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|t < 2.086 |

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|15 |

|In testing the hypotheses [pic][pic] , the following information is known: n = 64, [pic] = 78, and [pic] = 10. The test statistic is equal to: |

|a. |

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|+1.96 |

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|b. |

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|+2.4 |

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|c. |

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|-2.4 |

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|d. |

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|–1.96 |

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|16 |

|Which of the following p-values will lead us to reject the null hypothesis if the level of significance [pic] 0.05? |

|a. |

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|0.025 |

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|b. |

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|0.05 |

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|c. |

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|0.10 |

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|d. |

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|0.20 |

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|17 |

|For an F distribution, the number of degrees of freedom for the denominator |

|a. |

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|must be larger than the number of degrees of freedom for the numerator |

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|b. |

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|must be equal to the number of degrees of freedom for the numerator |

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|c. |

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|must be smaller than the number of degrees of freedom for the numerator |

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|d. |

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|can be larger, smaller, or equal to the number of degrees of freedom for the numerator |

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|18 |

|If a sample has 15 observations and a 95% confidence estimate for [pic] need to be constructed, the appropriate t-score is 2.131 |

|True |

|False |

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|19 |

|Given the significance level 0.05, the F-value for the degrees of freedom [pic] =5 and [pic] = 8, is 4.82. |

|True |

|False |

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|20 |

|In a regression problem the following pairs of (x, y) are given: (4,1), (4,-1), (4,0), (4,-2) and (4,2). That indicates that: |

|a. |

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|The correlation coefficient is –1 |

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|b. |

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|The correlation coefficient is 0 |

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|c. |

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|The correlation coefficient is 1 |

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|d. |

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|The coefficient of determination is between –2 and 2 |

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|21 |

|In a simple linear regression problem, the least squares line is [pic] = 2.73 - 1.02 [pic] , and the coefficient of determination is 0.7744. |

|The correlation coefficient must be –0.88. |

|True |

|False |

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