Hypothesis test for means is a statistical procedure that is used to compare the mean of population based on a sample with a given hypothesized value. There are two main conditions that must hold; the sample must have been selected randomly from the population and the population from which the sample was drawn must be distributed normally. It involves for key steps; hypothesis statement, analysis planning, data analysis and result interpretation.
In formulating the hypotheses, both the null and alternate hypothesis should be stated. The null states what we do not expect to find while the alternate hypothesis states what expect to find. If we are only interested in whether the population mean is different from the hypothesized mean then it is a two tailed test. The null hypothesis (H0) will be that the population mean and hypothesized mean are equal while the alternate hypothesis will be that the two means are unequal. If our interest is whether the mean of the population mean is greater than that of the hypothesized mean or the mean of the population mean is lesser than the hypothesized mean then it is one tailed test.
When forming the analysis plan the significance level should be selected. The commonly used significance levels are 1 percent, 5 percent, and 10 percent. The test method is the z-test for the mean. For a two-tailed tailed the significance level is divided into two in determining the z-critical since it can be both greater than or less than. However, for one tailed test we are only interested in one region. The figures below show the two tailed and one tailed test curves at 5 percent significance level.
Source: Itcconline
Source: Itcconline
In data analysis, the t statistic is computed by dividing difference between the population mean and the hypothesized mean with estimated standard error. The value is compared with the z-critical that is obtained from z-table. If it is higher than the z-critical we reject the null and choose the alternate hypothesis. If it was a two-tailed test then we conclude that the population mean is different from what we hypothesized.
Works Cited
For Dummies. How to Test Hypothesis Test for One Population Mean. n.d. <http://www.dummies.com/how-to/content/how-to-test-a-hypothesis-for-one-population-mean.html>.
ltcconline. Hypothesis Testing For a Population Mean. n.d. <https://www.ltcconline.net/greenl/courses/201/hyptest/hypmean.htm>.
Stattrek. Hypothesis Test for Mean. n.d. <http://stattrek.com/hypothesis-test/mean.aspx?Tutorial=AP>.
