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Final Exam Practice!

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  • If boys and girls are equally likely, groups of 400 births have a mean of 200 girls and a standard deviation of 10 girls. Is 232 girls in 400 births an unusually high number of girls?
    Yes
  • Assume that the percentage of people in a population have the following color eyes: 40% brown, 35% blue, 12% green, 7% gray, 6% hazel. If two people are randomly selected, what is the probability that at least one of them has brown eyes?
    0.64
  • If you plan to use a 0.05 significance level in a test of correlation between the systolic and diastolic readings, what are the critical values of r?
    +- 0.878
  • Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 100 (mmHg)
    (r = 0.867) There is a linear correlation, so we can use the regression equation. y = 1.31(100) + 43.56 y = 174.56
  • Construct a frequency distribution of the 20 brain volumes (cm3) listed below. Use the classes 900-999, 1000-1099, etc. What is the class width? What are the midpoints? What are the class boundaries?
    Class width: 100 Midpoints: 949.5, 1049.5, 1149.5, 1249.5, 1349.5, 1449.5 Boundaries: 898.5-999.5, 999.5-1099.5, etc.
  • Using the following sample data, find the z score corresponding to the eye height of 1642 mm. Is it unusual? Why/why not? :: 1550, 1642, 1538, 1497, 1571
    z = 1.54 :: This is not unusual because the value falls between 2 standard deviations of the mean
  • Use the following information to find the degrees of freedom, critical values and confidence interval estimate of sigma : 99% confidence; n=25, s=0.24mg.
    df = 24. chi-squareR = 45.559 chi-squareL = 9.886 Confidence Interval: 0.17 mg < sigma < 0.37 mg.
  • Solve:
    n = 752
  • If 1 adult female is randomly selected, find the probability that they have a mean overhead reach less than 205.0 cm.
    0.4768
  • Solve:
    Ho : µ = 3369g H1: µ < 3369g. Test statistic: t = -19.962. Critical value: t = -2.328. P-value < 0.005. Reject Ho
  • Construct a 95% confidence interval estimate of the mean discrepancy for the population of wristwatches
    -22.1 sec < µ < 308.1 sec
  • How many people are under 25?
    33
  • Construct a box-and-whisker diagram with the following list of data: 56, 78, 46, 83, 45, 67, 49, 68, 73, 85, 59, 56, 79, 48, 65, 42, 61, 83, 76, 51 (n=20)
    Min: 42, Q1: 50, Median: 63, Q3: 77, Max: 85
  • The following table lists overall quality scores and prices of 40-inch LCD TVs. Do these data suggest that you can get better quality by spending more? Use alpha = 0.05.
    r = 0.739. Critical values: -0.786, 0.786. Fail to reject Ho
  • Solve:
    1.2¢
  • Find the probability of randomly selecting 1 of the 839 challenges and getting a challenge that was accepted, given that it was made by a female player.
    126 / 350 or 0.360
  • What value has a probability of 0.3782 if the mean is 0 and the standard deviation is 1? What type of distribution is this?
    Z = -0.31
  • A fan of Lady Antebellum music plans to make a custom CD with 12 of their 27 songs. How many different combinations of 12 songs are possible? Is it practical to make a different CD for each possible combination?
    17,383,860. Not practical
  • Listed below are numbers of enrolled students and numbers of burglaries for randomly selected large colleges in a recent year. Can we conclude that there is a linear correlation between enrollment and burglaries? Use ∝ = 0.05
    r = 0.561. Critical values: r = +- 0.632. P-value = 0.091. Fail to reject Ho
  • Solve:
    a. Ho : p = 0.5 H1: p > 0.5 b. z = 6.33
  • If 1 of the subjects is randomly selected, find the probability of selecting someone who entered a plea of not guilty or was not sentenced to prison.
    0.619
  • Solve:
    $315,075. The offer is well below the expected value, so she should continue
  • Find the probability of randomly selecting 1 of the 839 challenges and getting a challenge that was accepted and was made by a female player.
    126 / 839 or 0.150
  • Solve:
    Ho: sigma= 567g. H1: sigma≠ 567g. Test statistic: chi-square = 54.038. Critical values of chi-square: 51.172 and 116.321. 0.02 < P-value < 0.05. Fail to reject
  • Solve:
    Ho: µ = 24. H1: µ < 24. Test statistic: t = -7.323. Critical value: t = -1.685. P-value < 0.005. Reject Ho
  • A presidential candidate plans to visit the capitals in 4 of the 50 states. What is the probability that she selects the route of Sacramento, Albany, Juneau, and Hartford? Is it practical to list all of the different possible routes?
    1 / 5,527,200. No, there are too many possibilities - it is not practical.
  • Solve:
    61.5% < p < 66.5% :: Interval is above 50%, so majority consume alcoholic beverages
  • What is the frequency for class 4.5-6.5?
    30
  • Calculate the student's GPA. Round to the nearest hundredth.
    GPA: 2.82
  • If 49 adult females are randomly selected, find the probability that they have a mean overhead reach less than 207.0 cm.
    0.8888 (tech: 0.8889)
  • What percentage of people are between 35-39? Round to one decimal.
    11.3%