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    Quiz 3 Hypothesis Testing

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    Manoj Mudiraj
    The document contains 3 examples of hypothesis testing using a t-test. The first example finds no significant difference between population means. The second finds no significant difference between mathematical anxiety levels of male and female computer science students. The third finds no significant difference between mean hourly rates from two cities. Each example states the hypothesis, level of significance, t-test calculation, decision rule, and conclusion.

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    Quiz 3 Hypothesis Testing

    Uploaded by

    Manoj Mudiraj
    128 views7 pages
    The document contains 3 examples of hypothesis testing using a t-test. The first example finds no significant difference between population means. The second finds no significant difference between mathematical anxiety levels of male and female computer science students. The third finds no significant difference between mean hourly rates from two cities. Each example states the hypothesis, level of significance, t-test calculation, decision rule, and conclusion.

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    The document contains 3 examples of hypothesis testing using a t-test. The first example finds no significant difference between population means. The second finds no significant difference between mathematical anxiety levels of male and female computer science students. The third finds no significant difference between mean hourly rates from two cities. Each example states the hypothesis, level of significance, t-test calculation, decision rule, and conclusion.

    Copyright:

    © All Rights Reserved
    Download as DOCX, PDF, TXT or read online from Scribd
    Download as docx, pdf, or txt
    128 views7 pages

    Quiz 3 Hypothesis Testing

    Uploaded by

    Manoj Mudiraj
    The document contains 3 examples of hypothesis testing using a t-test. The first example finds no significant difference between population means. The second finds no significant difference between mathematical anxiety levels of male and female computer science students. The third finds no significant difference between mean hourly rates from two cities. Each example states the hypothesis, level of significance, t-test calculation, decision rule, and conclusion.

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    © All Rights Reserved
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    Download as docx, pdf, or txt
    of 7

    NAME : Vaishnavi peddineni COURSE; BS BIO 1-1

    STUDENT ID : 20-2-01513 DATE: 05-07-2021

    1)Step 1: State the hypothesis


    H 0: There is no significant difference between the population
    mean.
    µ1 -µ2 =0
    H1: There exist a significant difference between the
    population mean.

    µ1 -µ2 ≠ 0

    Step 2: Level of significance α


    = 0.01
    Degree of freedom, df = n1 + n2 - 2
    = 1 + 28 -2
    =44
    Critical region, tcritical= ±2.414 This
    is a two tailed test.

    Step 3: Compute the value of t test


    𝑥̅1= 62.4 n1= 18 s1= 13.5
    𝑥̅2= 67.2 n2= 28 s2= 11.8

    tcomputed (𝑥̅1−𝑥̅2)−𝐷𝑜

    Here,sp2 = ( 𝑛1−1)𝑠1𝑧

    + (𝑛2−1)𝑠22 𝑛1+𝑛2−2

    1 + 28 − 2
    = (18 − 1)13.52 + (28 − 1)11.82

    = 155.79

    tcomputed

    = -1.265

    Step 4: Decision rule


    Computed t value is less than the critical value, so we cannot reject the
    nullhypothesis. Step 5: Conclusion
    At α = 0.01, there is no significant difference between the population
    mean.

    2) Step 1: State the hypothesis


    H0: There exist no significant difference between the mean
    mathematical anxiety experienced by male and female computer
    science students. µ1 -µ2 =0
    H 1: There exist a significant difference between the mean
    mathematical anxiety experienced by male and female computer
    science students. µ1 -µ2 ≠ 0

    Step 2: Level of significance


    α = 0.05
    Degree of freedom, df = n1 + n2 - 2
    = 23 + 27 -2
    = 48

    Critical region, tcritical= ±1.677 This


    is a two tailed test.

    Step 3: Compute the value of t test

    𝑥̅1= 38.4 n1= 23 s1= 11


    𝑥̅2= 42.7 n2= 27 s2= 12.3

    tcomputed (𝑥̅1−𝑥̅2)−𝐷𝑜

    Here, sp2 = (
    𝑛1−1)𝑠12 + (𝑛2−1)𝑠22
    𝑛1+𝑛2−2

    =
    = 137.41

    tcomputed

    =
    = -1.293
    Step 4: Decision rule
    Computed t value is less than the critical value, so we cannot
    reject the null hypothesis.
    Step 5: Conclusion
    At α = 0.05, there exist no significant difference between the mean
    mathematical anxiety experienced by male and female
    computer science students.

    3) Step 1: State the hypothesis


    H0: There is no significant difference in the mean hourly rates
    from two cities. µ1 -µ2 =0
    H 1: There is significant difference in the mean hourly rates
    from two cities. µ1 -µ2 ≠ 0
    Step 2: Level of significance α
    = 0.10
    Degree of freedom, df = n1 + n2 - 2
    = 8 + 8 -2
    = 14
    Critical region, tcritical= ±1.345 This
    is a two tailed test.

    Step 3: Compute the value of t test

    𝒙𝟏 𝒙𝟐 (𝒙𝟏 − ̅𝒙1)2 (𝒙𝟐 − ̅𝒙2)2

    190 198 252.02 862.89

    140 150 1164.52 346.89


    150 130 582.02 1491.89

    212 156 1434.52 159.39

    208 175 1147.52 40.64

    178 160 15.02 74.39

    135 180 1530.76 129.39

    180 200 34.52 984.39

    Total: 1393 1349 6160.9 4089.87

    • ∑𝑥1 = 1393

    • ∑𝑥2 = 1349

    • 𝑥1̅ = = 174.125

    • 𝑥̅2= 168.625

    • ∑(𝑥1 − 𝑥1)2 = 6160.9

    • ∑(𝑥2 − 𝑥̅2)2= 4089.87

    • s ̅

    = 29.667
    So, 𝑠𝐼2 = (29.667)2 = 880.13

    • 𝑠 ̅

    = 24.172

    So, 𝑠𝐼2 = (24.172)2 = 584.24

    • tcomputed=

    𝑥̅1= 174.125 n1= 8 s1= 29.667


    𝑥̅2= 168.625 n2= 8 s2= 24.172

    tcomputed (𝑥̅1 − 𝑥̅2) − 𝐷𝑜

    Here, sp2 = (
    𝑛1−1)𝑠12 + (𝑛2−1)𝑠22
    𝑛1+𝑛2−2

    =
    = 73.185

    tcomputed
    =

    = 0.406

    Step 4: Decision rule


    Computed t value is less than the critical value, so we cannot
    reject the null hypothesis.
    Step 5: Conclusion
    At α = 0.10, there exist no significant difference in the mean hourly rate
    from two cities.

    THANK YOU

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