Statistical Significance The power of ALPHA The decisive

Statistical Significance The power of ALPHA

The decisive value of P is called the significance level. We write it as α, the Greek letter alpha. “Significant” in the statistical sense does not mean “important. ” It means simply “not likely to happen just by chance. ”

Statistical Significance If the P-value is as small as or smaller than alpha, we say that the data are statistically significant at level α. In practice, the most commonly used significance level is: α = 0. 05

To test the hypothesis H 0: μ= μ 0 based on an SRS of size n from a population with unknown mean μ and known standard deviation σ, compute the one-sample z statistic z= x-ℳ σ/√n

Step 1: Hypotheses Identify the population of interest and the parameter you want to draw conclusions about. State hypotheses. Step 2: Conditions Choose the appropriate inference procedure. Verify the conditions for using it. Step 3: Calculations If the conditions are met, carry out the inference procedure. • Calculate the test statistic. Find the P-value. Step 4: Interpretation Interpret your results in the context of the problem. • Interpret the P-value or make a decision about H 0 using statistical significance. Don't forget the 3 C's: conclusion, connection, and context.

reject H 0 or fail to reject H 0 we will reject H 0 if our result is statistically significant at the given α level. That is, we will fail to reject H 0 if our result is not significant at the given α level. EXAMPLE T C E Ho: µ = 0, there is NO difference in job satisfaction between the two work environmen REJ Ho: µ ≠ 0, there is a difference in job satisfaction between the two work environments α =. 05 p =. 0234 Therefore, our hypothesis testing for this particular case is statistically significant at α =. 05

A certain random number generator is supposed to produce random numbers that are uniformly distributed on the interval from 0 to 1. If this is true, the numbers generated come from a population with μ = 0. 5 and σ = 0. 2887. A command to generate 100 random numbers gives outcomes with mean x = 0. 4365. Assume that the population σ remains fixed. We want to test H 0: μ= 0. 5 versus Ha: μ ≠ 0. 5. (a) Calculate the value of the z test statistic and the P-value. (b) Is the result significant at the 5% level (α = 0. 05)? Why or why not? (c) Is the result significant at the 1% level (α = 0. 01)? Why or why not? (d) What decision would you make about H 0 in part (b)? Part (c)? Explain.

(a) Calculate the value of the z test statistic and the P-value. (b) Is the result significant at the 5% level (α = 0. 05)? Why or why not? Since the P-value is less than 0. 05, we say that the result is statistically significant at the 5% level. (c) Is the result significant at the 1% level (α = 0. 01)? Why or why not? Since the P-value is greater than 0. 01, we say that the result is not statistically significant at the 1% level.

(d) What decision would you make about H 0 in part (b)? Part (c)? Explain. At the 5% level, we would reject Ho and conclude that the random number generator does not produce numbers with an average of 0. 5. At the 1% level, we would not reject Ho and conclude that the observed deviation from the mean of 0. 5 is something that could happen by chance. That is, we would conclude that the random number generator is working fine at the 1% level