The z-statistic of the Brett's data is -5.30
The formula for the test statistic depends on whether the population standard deviation (σ) is known or unknown. If σ is known, our hypothesis test is known as a z test and we use the z distribution
The standard deviation is a measure of the amount of variation or dispersion of a set of values.
Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.
Given,
Population Mean = 310
Standard deviation = 20
Sample data mean = 295
Sample size =50
z-statistic = (Sample data mean - Population mean) / (Standard deviation /[tex]\sqrt{sample size}[/tex])
z-statistic = [tex]\frac{295-310}{20/\sqrt{50} } =-5.30[/tex]
Hence, the z-statistic for Brett's data is -5.30
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