# Which hypothesis test to perform?

Based on the data, can we conclude that the mean intraocular pressure of the population differs from 14 mm Hg?Step 1: Testing MethodThe test we need to use is a one sample t-test for means (Hypothesis test for means is a t-test because we don’t know the population standard deviation, so we have to estimate it with the sample standard deviation s).Step 2: AssumptionsList all the assumptions for your test to be valid..Even if assumptions are not met, we should comment on how that would affect our results.• The dependent variable must be continuous.• The observations are independent of one another.• The dependent variable should be approximately normally distributed.• The dependent variable should not contain any outliers.Step 3: HypothesesThe null hypothesis describes a claim about the population mean..Hence, the null hypothesis states that the population mean of the intraocular pressure is 14 mm Hg and the alternate hypothesis states that the population mean of the intraocular pressure differs from 14 mm Hg..It can be mathematically formulated as follows:Step 4: Calculate the test statisticȳ = sample mean = 15.623s = sample standard deviation = 3.382n = 21μ = 14Substituting the values, we get, t = 2.199In this case (two-tailed), the p-value is the area in both tails of the t distribution.Step 5: Determine p-value and compare with the significance levelAfter computing the test statistic, now we can compute the p-value (using the t-table)..The corresponding p-value for the t statistic is 0.0398.So, what is the p-value?.It is the chance of observing your sample results or more extreme results assuming that the null hypothesis is true..If this chance is ‘small’, we may reject the null hypothesis.In our example, the p-value is the probability of observing a sample mean of 15.623 mm Hg, or a value more extreme, assuming the true mean pressure is 14 mm Hg.With a p-value = 0.0398, which is less than 0.05 (our chosen significance level), we reject the null hypothesis..There is sufficient sample evidence to conclude that the true mean intraocular pressure differs from 14 mm Hg.We can implement the one sample t-test in Python by using the scipy module.Output :Connect on LinkedIn.. More details