Z Tests Lecture

IV is Nominal

DV is Interval

Today we will discuss, 2 and 1 tail Z tests, 2 and 1 tail Tests. These tests are designed to measure the significance of the results of a comparison of 2 means. In other words, we are looking to identify a relationship between the Independent variable (nominal level of measurement) and the dependent variable (interval level of measurement). Please do not confuse the Z-score and Z-test. Before I go into these formulas, I want to cover the Hypothesis statement.

The hypothesis (H1) is always a statement of equality because the researcher starts the research assuming all variables are equal.

We can take the following statement and make a hypothesis (H1) and an Alternative hypothesis (Ha) from the information given

A group of middle-aged men (50 in sample) was asked to complete a questionnaire on their attitudes toward work and family. Each of these men is married and has at least 2 children. Another group of men who have no children also completed the same survey.

H1: Attitudes toward work and family will be the same for middle-aged men who have children as for those who do not.

Ha: The attitudes toward work and family will differ between middle-aged men who have children and those who do not.

Let's move into showing (or attempting to show) a relationship between the independent and dependent variable mathematically (not the previous example). I will be covering the Z Test and T Test, these are Parametric tests:

There is a 5 step process to setting up a statistical hypothesis:

1. Set up the hypothesis (H1) and alternative hypothesis (Ha): EXAMPLE

H1: μ = 32

Ha: μ ≠ 32

2. Pick the confidence level (I am 95% sure there is a relationship) and place the alpha (based on the chart in your book) Ü so for 95% (2 tail test) would be Ü= 1.96 We will use this level most of the time, I will refer to it as your Stat critical and we will compare it to your Stat calculated to identify significance. In addition, to be significant or to show a relationship, the Stat calculated must be greater than or equal to the Stat critical. In this case it must be greater than 1.96.

3. Calculate the Test statistic (formula which is appropriate for the variables involved)

4. Decided whether or not to reject the Hypothesis (H1)

5. Put in plain English so a 5th grader can understand

Now, we will apply this process in a moment after I introduce our first formula. It is called a Z test (a brother to your Z score in Research 341) and it is used for 2 variable sample populations whereby the Independent variable is a Nominal level of measurement and the Dependent variable is an Interval level of measurement.

The rules to engage a Z test are:

Z TEST: Requirements

1. The observations must be independent of one another. One way to assure independence is simple random selection.

2. The sample size must be large n>30 so that the distribution of sample means can be regarded as a normal distribution.

3. The population standard deviation must be known.

4. Independent variable is a Nominal level of measurement and the Dependent Variable is an Interval level of measure ment

_

The formula is Z = X - μ

σ/√n

_

X= Is the sample mean of the population

μ = Is the population mean

σ = Is the population standard deviation

n = is the number in our sample ( > than 30)

Ü = is our rejection region, we can say that we are 95% confident that there is a relationship between the independent and dependent variable

(Ü = .05). Therefore our confident level is 1.96 (based on chart on the Z-table I gave you)

Let's do the example

A Computer Company is conducting a yearly quality assurance process on their customer service department. Based on Industry Research, it is reported that customers will wait on the phone for 7 minutes for customer service assistance. The organization wants to establish the 7 minute bench mark for their customer service department.

As a result, The organization wants to know if the true hold time is 7 minutes for their customers waiting on the phone for their organization's customer service representative. In other words, they feel that their customers are waiting 7 minutes for a customer service operator and NOT longer or shorter. In this problem, we are given the sample mean:

_

X of 7.12 minutes, the population standard deviation s of 2 minutes and 50 (n) customers were monitored while they waited on the phone for a company operator.

_

X= 7.12 minutes

μ = 7 minutes (company's claim)

s = 2 minutes (substitute s for σ)

n = 50 customer calls were monitored

Ü = .05 or we can say that the company is 95% confident that customers stay on the phone for 7 minutes

Step 1:

H1: μ = 7 minutes

Ha: μ ≠ 7 minutes

Step 2: