Exam 1

  1. Metainformation

    Tag Value
    fileInferential_Statistics_eur-inferential_statistics-204-en_eur-inferential_statistics-204-en
    nameeur-inferential_statistics-204-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 .31 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−.31=1.662se_m = 2 \times \sqrt {1-.31} = 1.662

    95%CI=5.2±1.96×1.662=5.2±3.2695\% CI = 5.2 ± 1.96 \times 1.662 = 5.2 ± 3.26

    The 95% CI of grade 5.2 is [1.94−8.46][1.94-8.46]