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    Sample Problems

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    Problems in Hypothesis testing 2 samples

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    Sample Problems

    Uploaded by

    kelvin
    493 views2 pages
    Problems in Hypothesis testing 2 samples

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    Problems in Hypothesis testing 2 samples

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    © All Rights Reserved
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    Download as docx, pdf, or txt
    493 views2 pages

    Sample Problems

    Uploaded by

    kelvin
    Problems in Hypothesis testing 2 samples

    Copyright:

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

    MARIKINA POLYTECHNIC COLLEGE

    Undergraduate School (Step 3) Compute for test statistic

    “Sample problems in Hypothesis Testing (Two Samples) The formula for t computed requires the mean of
    our samples.
    Problem #1 1 1
    PETA or the Philippine Ethical Treatment for x1 
    n
     x   540   108
    5
    Animals claims that the mean daily costs of food for dogs
    1 1
    and cats are the same. The results for samples of the two x2   x   545   109
    types of pets are show below. At 5% level of significance, n 5
    is there sufficient evidence to support the claim?
    x1  x2 108  109
    Cats 125 110 105 100 100 t   0.2
    Dogs 115 110 110 105 105 2 2
    s s 108.75 17.5
    1
     2 
    n1 n2 5 5
    Solution:
    Since the population variance of each group is not
    given and the sample sizes are less than 30, hence we will i.e. tcomputed  0.2
    use t-test. The claim is “the mean daily cost of food for
    dogs and cats are the same”. (Step 4) Decision
    Since the computed t value of -0.2 is greater than
    (Step 1) State the null and alternative hypotheses -2.57, hence the decision is not to reject the null
    hypothesis.
    Hₒ: 1  2 , The mean daily cost of food for dogs and
    cats are the same. (claim) (Step 5) Conclusion
    Hₐ: 1  2 , The mean daily cost of food for dogs and At 5% level of significance, there is sufficient
    evidence to support the claim that the mean daily cost of
    cats are not the same.
    food for dogs and cats are the same.
    (Step 2) Determine the critical value(s)
    Problem #2
    The economist wants to prove that there is
    Since we are in t-test, we need to consider the
    significant difference between the mean hourly rates
    degrees of freedom, and the level of significance. First,
    charged by automobile mechanics in Manila and Quezon
    we will determine the variance of each group.
    City. The population variance of the hourly rates for each
    city is 703.93 (Manila) and 698.87 (Quezon). He
     x  x 
    2
    435 randomly selects 10 auto repair facilities from both cities
    s2
       108.75
    n 1 and record their hourly rates (in pesos). For instance the
    1
    4
    computed mean hourly rates for Manila and Quezon City
     x  x 
    2
    70
    2
    s    17.5 is 170 pesos and 165 pesos respectively. At 5% level of
    n 1
    2
    4 significance, is there sufficient evidence to support the
    Use rule of thumb to decide whether to assume claim of the economist?
    the population variances are equal or not.
    s1 Solution:
    0.5   2 Since the population variance of each group is
    s2
    given hence we can use z-test. The claim is “There is
    0.5  10.43  2 significant difference between the mean hourly rates
    4.18
    charged by automobile mechanics in Manila and Quezon
    0.5  2.5  2
    City”.
    Since the computed ratio did not meet the
    requirement, hence we will assume that the population
    Hₒ: 1  2 , There is no significant difference between
    variances are not equal. Compute for the degrees of
    freedom. (Round down the result) the mean hourly rates charged by automobile mechanics
    in Manila and Quezon City.
    2 Hₐ: 1  2 , There is significant difference between the
     s12 s22   108.75 17.5 
    2

          mean hourly rates charged by automobile mechanics in


    df   12 2  2  
    n n 5 5 
    2 2
     5.25  5 Manila and Quezon City. (claim)
     s12   s22   108.75   17.5 
            (Step 2) Determine the critical value(s)
     n1    n2   5   5 
    Since the level of significances is 5% and we have
    n1  1 n2  1 5 1 5 1
    two tailed test, hence the critical z value is ±1.96

    Using the t distribution table we will have ±2.57 i.e. zcritical  1.96
    i.e. tcritical  2.57
    (Step 3) Compute for test statistic The claim is “there is significant relationship between the
    number of employees and the production units”
    x1  x2 170  165 (Step 1) State the null and alternative hypotheses
    z   0.42 Hₒ:   0 , There is no significant relationship between
    12 22 703.93 698.87

     the number of employees and the production units.
    n1 n2 10 10
    Hₐ:   0 , There is significant relationship between the
    i.e. zcomputed  0.42 number of employees and the production units. (claim)

    (Step 4) Decision (Step 2) Determine the critical Values


    Since the computed z value of 0,42 is greater than Since the degrees of freedom is df = 5 – 2 = 3 and
    the critical z value of -1.96, hence the decision is not to the level of significance is 5%, hence the critical t values
    reject the null hypothesis. are ±3.18

    (Step 5) Conclusion (Step 3) Determine the test statistic


    At 5% level of significance, there is not sufficient n2 3
    evidence to support the claim that there is significant tr  0.77  2.09
    difference between the mean hourly rates charged by
    1 r 2
    1  0.772
    automobile mechanics in Manila and Quezon City.
    (Step 4) Decision
    “Sample Problems in Correlational Analysis” The computed t value of 2.09 is less than the
    critical t values of 3.18, hence the decision is not to reject
    Problem #1 the null hypothesis.
    The production department of WSS Electronics
    wants to explore the relationship between the numbers of (Step 5) Conclusion
    employees who assemble a certain product and the At 5% level of significance, there is not sufficient
    number of units produced per hour. The complete set of evidence to support the claim that there is significant
    paired observations follows: relationship between the number of employees and the
    production units.
    Number of Production
    Employees (x) (units) (y)
    2 20
    4 15
    6 25
    8 28
    5 22
    Determine the coefficient of correlation using
    pearson and test the significance at 5% level of
    significance.

    Solution:
    Compute for the coefficient of correlation using
    pearson.

    (x) (y) x² y² xy
    2 20 4 400 40
    4 15 16 225 60
    6 25 36 625 150
    8 28 64 784 224
    5 22 25 484 110
    25 110 145 2518 584

    n xy    x   y 
    r
     n x 2   x 2   n y 2   y 2 
           
    5  584    25 110 

    5 145    25 2  5  2518   110 2 
      
    r  0.77

    Interpretation: The computed r of 0.77 is interpreted as


    high correlation. It implies that as the number of
    employees increase, the production unit also increases.

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