Exam 1

  1. Metainformation

    Tag Value
    fileInferential_Statistics_eur-inferential_statistics-203-en_eur-inferential_statistics-203-en
    nameeur-inferential_statistics-203-en
    sectionInferential Statistics/Confidence Intervals/Margin of error, Inferential Statistics/Confidence Intervals/Width
    typestring
    solution""
    TypeCalculate
    ProgramCalculator
    LanguageEnglish
    LevelStatistical Literacy

    Question

    Calculate the 95% Confidence Interval of a student who has a grade of 5.2 given a reliability of .81 for the exam. The variance of the grades is 4 Formula for the 95% confidence interval: 95%CI=Xo±Zp=95×sem95\% CI = X_o ± Z_{p=95} \times se_m Formula for standard error of measurement is: sem=so×1−Rxxse_m = s_o \times \sqrt{1 - R_{xx}}


    Solution

    You will need the formula for the 95% confidence interval: 95%CI=Xo±Zp=95×sem95\% CI = X_o ± Z_{p=95} \times se_m

    95%CI=5.2±1.96×sem95\% CI = 5.2 ± 1.96 \times se_m

    sem=2×1−.81=.872se_m = 2 \times \sqrt {1-.81} = .872

    95%CI=5.2±1.96×.872=5.2±1.7195\% CI = 5.2 ± 1.96 \times .872 = 5.2 ± 1.71

    The 95% CI of grade 5.2 is [3.49−6.93][3.49-6.93]