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    Hypothesis testing and level of measurement

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    IDENTIFYING LEVEL OF MEASUREMENT

    There are four levels of measurement, two are numeric and two are attribute data. This first time around, try to identify if a question produces a number or a text number. This not always an easy as you will see. This will be needed later when choosing a hypothesis test. Please attached, I attached the wrong file in a earlier request and a portion was missing.

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    https://brainmass.com/statistics/hypothesis-testing/hypothesis-testing-level-measurement-226990

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    Please see the attachment.

    IDENTIFYING LEVEL OF MEASUREMENT

    There are four levels of measurement, two are numeric and two are attribute data. This first time around, try to identify if a question produces a number or a text number. This not always an easy as you will see. This will be needed later when choosing a hypothesis test.

    Each of these are ONE question on a survey. Is that response an attribute or numeric value?

    1. Age:
    0 to 5 years old
    6 to 10 years old
    11 to 15 years old
    16 to 20 years old
    21 to 25 years old
    Attribute or Numeric? Numeric

    2. Gender:
    Male ______
    Female ______
    Attribute or Numeric? Attribute

    3. Annual Income to the nearest dollar _________ Numeric
    Attribute or Numeric?

    4. Your level of Education:
    Below a Bachelor's Degree _______
    Bachelor's or Master Degree _______
    Beyond a Master's Degree _______
    Attribute or Numeric? Attribute

    5. Number of years of formal education beyond high school ______ Numeric
    Attribute or Numeric?

    6. Emotional Intelligence is the single most important characteristic to leadership:
    Strongly Agree Agree No Opinion Disagree Strongly Disagree
    Attribute or Numeric? Attribute

    7. Emotional Intelligence is the single most important characteristic to leadership:
    (1=Strongly Agree, 2=Agree, 3=No Opinion, 4=Disagree, 5= Strongly Disagree)
    1 2 3 4 5
    Attribute or Numeric? Numeric

    HYPOTHESIS TEST ~ STUDENT T

    An auditor reviewed 25 insurance claims from a particular surgical office, determining that the mean out-of-pocket patient billing above the reimbursed amount was $275.66 with a standard deviation of $78.11. At the 5% level of significance, does this sample prove a violation of the guideline that the average patient should pay no more than $250 out-of-pocket?

    A. Write the Hypothesis

    H0: The mean out-of-pocket patient billing above the reimbursed amount ≤$250.
    H1: The mean out-of-pocket patient billing above the reimbursed amount >$250.

    B. Specify the Decision Rule
    Reject the null hypothesis, if the calculated value of test statistic is greater than the critical value of t at 0.05 significance level

    C. Calculate the Test Statistic
    The test statistic used is

    t Test for Hypothesis of the Mean
    Data
    Null Hypothesis = 250
    Level of Significance 0.05
    Sample Size 25
    Sample Mean 275.66
    Sample Standard Deviation 78.11

    Intermediate Calculations
    Standard Error of the Mean 15.622
    Degrees of Freedom 24
    t Test Statistic 1.642555371

    Upper-Tail Test
    Upper Critical Value 1.710882067
    p-Value 0.05675728
    Do not reject the null hypothesis
    D. Make the Decision
    Do not reject the null hypothesis
    E. Give an interpretation of the Decision
    Conclusion: Fails to reject the null hypothesis. The sample does not provide enough evidence to support the claim the mean out-of-pocket patient billing above the reimbursed amount is greater than $250.
    F. P-value Method
    1. Calculate the P-value, what is it?
    P value =P(T>1.6425)= 0.05675728

    A p-value is a measure of how much evidence we have against the null hypothesis. The p-value measures consistency by calculating the probability of observing the results from your sample of data or a sample with results more extreme, assuming the null hypothesis is true. The smaller the p-value, the greater the inconsistency. Traditionally, researchers will reject a hypothesis if the p-value is less than 0.05. The general rule is that a small p-value is evidence against the null hypothesis while a large p-value means little or no evidence against the null hypothesis. Here the p value is 0.05675728. Thus there is not much evidence against the null hypothesis.

    2. Does that P-value support the Decision in Part D?

    The p value approach also leads to the same ...

    Solution Summary

    The solution provides step by step method for the calculation of test statistic. Formula for the calculation and Interpretations of the results are also included.

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