# Hypothesis testing and level of measurement

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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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.