A recent study of 100 social workers in a southern state found that their mean salary was $23,000 with a standard deviation of $2100. A similar study of 95 social workers in a western state found that their mean salary was $34,200 with a standard deviation of$3200. Find the test statistic and critical value when the claim that the mean salaries of social workers in the western state is greater than that of social workers in the southern state. Use α = 0.05. Sample1: Social workers in a southern state, Sample2: Social workers in awestern state. a) Find the test statistic b) Find critical value
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
A recent study of 100 social workers in a southern state found that their
Sample1: Social workers in a southern state, Sample2: Social workers in awestern state.
a) Find the test statistic
b) Find critical value
a). Sample1-
sample size=
sample mean=$23000=
population mean=
Sample2-
sample size=
sample mean==$34200
population mean=
hypotheses to be tested here will be,
So, the test statistic will be given by,
where
Therefore, s=2692.486
Value of t under null hypothesis is -29.029
So,
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