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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.

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

#### Solution Preview

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?

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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