Employees in a large computer firm claim that the mean salary of the firm’s programmers is less than that of its competitors. The competitor’s salary is $47,000. A random sample of 30 of the firm’s programmers has a mean salary of $46,500 with a standard deviation of 5500. Calculate the test statistic for the hypothesis: Ho: mean >= 47000, H1: mean < 47000
Using the z-test formula to find the test statistic:
z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)
z = (46500 - 47000)/(5500/√30)
z = ?
Finish the calculation.
To calculate the test statistic for this hypothesis test, you can use the t-test formula:
t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
In this case, the sample mean is $46,500, the population mean (from the null hypothesis, Ho) is $47,000, the sample standard deviation is 5500, and the sample size is 30.
Plugging these values into the formula:
t = (46500 - 47000) / (5500 / sqrt(30))
Simplifying further:
t = -500 / (5500 / sqrt(30))
Calculating sqrt(30):
t = -500 / (5500 / 5.48)
t = -500 / 1016.667
t ≈ -0.492
Therefore, the test statistic for this hypothesis test is approximately -0.492.