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    One Sample T-Test

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    Prashant Singh
    The document contains summaries of several statistical tests performed on sample data: 1) A one-sample t-test is used to determine if the mean age of a sample is greater than 20, finding the null hypothesis is rejected. 2) A z-test is used to determine if the mean age differs from 23, finding enough evidence to conclude the population mean differs. 3) A one-way ANOVA test finds no significant difference in average handle times among three call operators. 4) A chi-square test examines the relationship between gender and political party preferences.

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    © All Rights Reserved
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    One Sample T-Test

    Uploaded by

    Prashant Singh
    25 views2 pages
    The document contains summaries of several statistical tests performed on sample data: 1) A one-sample t-test is used to determine if the mean age of a sample is greater than 20, finding the null hypothesis is rejected. 2) A z-test is used to determine if the mean age differs from 23, finding enough evidence to conclude the population mean differs. 3) A one-way ANOVA test finds no significant difference in average handle times among three call operators. 4) A chi-square test examines the relationship between gender and political party preferences.

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    8tests

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    The document contains summaries of several statistical tests performed on sample data: 1) A one-sample t-test is used to determine if the mean age of a sample is greater than 20, finding the null hypothesis is rejected. 2) A z-test is used to determine if the mean age differs from 23, finding enough evidence to conclude the population mean differs. 3) A one-way ANOVA test finds no significant difference in average handle times among three call operators. 4) A chi-square test examines the relationship between gender and political party preferences.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    25 views2 pages

    One Sample T-Test

    Uploaded by

    Prashant Singh
    The document contains summaries of several statistical tests performed on sample data: 1) A one-sample t-test is used to determine if the mean age of a sample is greater than 20, finding the null hypothesis is rejected. 2) A z-test is used to determine if the mean age differs from 23, finding enough evidence to conclude the population mean differs. 3) A one-way ANOVA test finds no significant difference in average handle times among three call operators. 4) A chi-square test examines the relationship between gender and political party preferences.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
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    of 2

    ONE SAMPLE T-TEST

    QUESTION : TEST TO DETERMINE (AT 5% LEVEL OF SIGNIFICANCE ) WHEATHER THE


    POPULATION MEAN AGE IS SIGNIFICANTLY GREATER THAN 20 GIVEN FOLLOWING AGES

    29 28 21 25 31 17 28 18 18 29 21 26 17 18 30 19 19 28

    ONE SAMPLE T-TEST

    SOLUTION:

    AGE DUMMY
    36 0 t-Test: One-Sample 28 0 21 AGE 25 Mean 23.83 31 Variance 34.15 17 Observations 18.00
    28 df 17.00 18 t Stat 17.30 18 P(T<=t) one-tail 0.00 29 t Critical one-tail 1.74 21 P(T<=t) two-tail

    0.00 26 t Critical two-tail 2.11 1718 Null Hypothesis is rejected as t stat value is greater than t

    critical one-t-tail 30 Null Hypothesis is rejected as P(T<=t) one-tail= 0.00 which is less than 0.05
    191928

    Z - TEST FOR ONE SAMPLE SAMPLE MEAN

    QUESTION: IS THERE ENOUGH EVIDENCE (AT 5% LEVEL OF SIGNIFICANCE ) TO


    CONCLUDE THAT THE POPULATION MEAN AGE DIFFERS SIGNIFICANTLY FROM 23 BASED
    ON THE FOLLOWING

    AGE DUMMY
    25 0 30 0 23 0 21 0 24 0 AGE 22 0 24 0 Mean 21.94 25 0 Standard Error 0.41 22 0 Median 22.00
    21 0 Mode 21.00 22 0 Standard Deviation 2.41 18 0 Sample Variance 5.82 20 0 Kurtosis 2.15 24 0
    Skewness 0.96 24 0 Range 12.00 22 0 Minimum 18.00 23 0 Maximum 30.00 19 0 Sum 768.00 21
    0 Count 35.00 20 0 Largest(1) 30.00 21 0 Smallest(1) 18.00 21 0 19 0 21 0 19 0
    24 0 25 0 20 0 20 0 z-Test: Two Sample for Means 23 0 22 0 AGE 23 0 Mean 21.94 19 0 Known
    Variance 5.82 22 0 Observations 35.00 19 0 Hypothesized Mean Difference 23.00 z -2.59 P(Z<=z)
    one-tail 0.00 z Critical one-tail 1.64 P(Z<=z) two-tail 0.01 z Critical two-tail 1.96

    ONE WAY ANNOVA


    A CALL CENTER MANAGER WANTS TO KNOW IF THERE IS A SIGNIFICANT DIFFERENCE IN
    AVERAGE HANDLE TIMES AMONGST THREE DIFFERENCE CALL OPERATORS.
    INDEPENDENT VARIABLE : CALL OPERATOR DEPENDANT VARIABLE : AVERAGE AVERAGE
    HANDLE TIME

    AVERAGE HANDLE TIMES (IN SECONDS) OPERATOR1 OPERATOR2 OPERATOR3


    76.50 74.50 72.50 76.00 74.50 75.20 HYPOTHESIS: 74.50 74.50 74.80 Ho: μ1=μ2=μ3 73.70
    74.20 76.00 Ha : AT LEAST ONE μ IS DIFFERENT 75.60 74.20 73.90 75.40 74.50 73.80 73.80
    73.40 75.30 76.10 74.20 75.80 74.10 75.20 74.90 75.10 75.60 75.10

    Anova: Single Factor

    SUMMARY
    Groups Count Sum Average Variance OPERATOR1 10.00 750.80 75.08 1.01 OPERATOR2 10.00
    744.80 74.48 0.35 OPERATOR3 10.00 747.30 74.73 1.11

    ANOVA
    Source of Variation SS df MS F P-value F crit Between Groups 1.82 2.00 0.91 1.10 0.35 3.35
    Within Groups 22.29 27.00 0.83

    Total 24.11 29.00

    CHI -SQUARE TEST

    RELATIONSHIP BETWEEN GENDER AND POLITICAL PARTIES

    OBSERVED FREQUENCY OIJ EIJ (OIJ-EIJ) (OIJ-EIJ)^2 (OIJ-EIJ)^2/EIJ


    WOMEN MEN TOTAL SP WOMEN 27 23.4 3.6 12.96 0.55 SP 27 10 37 MEN 19 13.6 5.4 29.16
    2.14 BSP 16 15 31 BSP WOMEN 16 19.6 -3.6 12.96 0.66 TOTAL 43 25 68 MEN 15 11.4 3.6
    12.96 1.14 TOTAL 4.50

    EXPECTED FREQUENCY
    WOMEN MEN TOTAL SP 23.40 13.60 37.00 BSP 19.60 11.40 31.00 TOTAL 43.00 25.00 68.00

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