for a sample of 12 items from a normally distributed population for which the standard deviation is = 17.0, the sample mean is 230.8. At the 0.05 level of significance, test Ho : μ ≤ 220 versus Hı: μ >220. Determine and interpret the p-value for the test.
business statistics - MathGuru, Thursday, July 30, 2009 at 9:00am
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 = (230.8 - 220)/(17/√12)
Finish the calculation. Since this sample is from a normally distributed population, use a z-table to determine your p-value (the p-value is the actual level of the test statistic). Compare the p-value to 0.05 level of significance for a one-tailed test (the test is one-tailed because H1 is showing a specific direction). Determine whether or not to reject the null based on your outcome. If the null is rejected, then you conclude µ > 220. If the null is not rejected, then you cannot conclude a difference.
I hope this will help get you started.