When the actual population mean of the students’ height in the college is 168 cm then the power of the test is the probability of making the correct decision. In the context of the given problem, we can interpret the power of the hypothesis as follows. Refer to the article on excel for normal distribution probabilities.įrom this, we get the power of the hypothesis test is 1-ß = 1-0.2382 = 0.7618. Here we use the excel formula to find the probability. Therefore, we need to find the standard normal probability. Note that the variable Z follows the standard normal distribution. Therefore, we get the probability of committing Type II error is as follows. Moreover, the actual population mean (µ) is 168 cm. Statistical power is the probability that a hypothesis test correctly infers that a sample effect exists in the population. H 1: µ Z c | µ M c | µ < µ 0) Step 4: Calculations Because we’re talking about determining the sample size for a study that has not been performed yet, you need to learn about a fourth considerationstatistical power. The null and alternative hypotheses for the one-sample Z test are as follows. Step 1: Fix the null and alternative hypotheses The power of a test is the probability of rejecting the null hypothesis when the alternative hypothesis is true, given a particular significance level. To know why did we choose the Z test in this context, please refer to the article on one sample mean test. Power of the test, specified as a scalar value in the range (0,1) or as an array of scalar values in the range (0,1). Therefore, we use a one-sample Z test to test the claim. We assumed that the population is normally distributed with the standard deviation is 12 cm. In this context, we need to test if the average of the student’s height is less than 172 cm. Therefore, we will set up the whole problem as follows. Solution:Ĭonsider the researcher’s point of view. Calculate the power of the hypothesis test if, in reality, the average height of students in the college is 168 cm. This report sho ws the calculated power for each scenario. The researcher assumed that the population is normally distributed with the standard deviation of heights of the students is 12 cm. A sample size of 10 achieves 14 power to detect a difference of 12.750 between the null hypothesis variance of 42.500 and the alternative hypothesis variance of 29.750 using a one-sided, Chi-Square hypothesis test with a significance level (alpha) of 0.050, assuming the mean is not known. He used a statistical hypothesis test to test if the average of the student’s height is less than 172 cm.
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