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The following table gives the partial results from a company sampling their employees to see how many years they had worked for the company. The data for both samples was right-skewed.

Department Quality assurance Service
Mean (years) 4.2 2.6
Standard deviation (years) 1.1 1.7

The company wants to use these results in a two-sample t test to see whether there is a significant difference between lengths of time for employees in the quality assurance and service departments.

Which of the following are conditions for this type of test?
Choose all answers that apply:


A. The samples represent no more than 10% percent of the employees in each department.


B. The sample includes equal numbers of employees from each department.


C. The sample includes at least 30 employees from each department.

Sagot :

Using the Central Limit Theorem, it is found that the condition that applies to this test is:

C. The sample includes at least 30 employees from each department.

What does the Central Limit Theorem state?

It states that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the sampling distribution is also approximately normal, as long as n is at least 30.

From this, since we have a skewed variable, it is found that a sample size of at least 30 is needed, hence option C is correct.

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

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