 Hello, this is a video on one sample hypothesis testing. Calculating the test statistic for a mean. Your sample consists of 47 subjects with a mean of 35.5 and a standard deviation of 1.49. Calculate the test statistic. You have the following hypotheses. The null hypothesis H0 is mu is equal to 36.1. The alternative hypothesis H sub 1 is equal to mu is less than 36.1. To calculate the test statistic for any hypothesis test, you need to use the appropriate formula. Since we are dealing with mu, a population mean, and we do not know the population standard deviation, we know the sample standard deviation but not a population standard deviation, our test statistic will be a t statistic. So we used a t distribution. So the formula for the test statistic for a population mean, when the standard deviation of the population is unknown is x bar minus mu divided by the standard deviation divided by the square root of n. So all of these variables are given to me in the question here. My sample consists of 47 subjects. So sample size is 47. The mean of the sample x bar is equal to 35.5. The standard deviation S of my sample is 1.49. And then my population mean, the value that I am dealing with here is mu is equal to 36.1. Plug in these four values into the test statistic formula. So you will have 35.5 minus 36.1 divided by 1.49 divided by the square root of 47. 35.5 minus 36.1 is negative 0.6. In the denominator down here, you have another fraction. You have 1.49 divided by square root of 47. And you wanna keep this answer to as many decimal places as possible. So I'll do 0.2173388. The more decimal places you keep, the more accurate your answer will be. The more the better. Then divide. Your test statistic is going to be negative 2.76. That is your test statistic in this case. Thanks for watching.