One Sample T-Test Example Problems With Solutions Pdf
Introduction
What is One Sample T-Test?
One-sample t-test is a statistical test used to determine whether a sample mean differs significantly from a hypothesized population mean. The test is based on the assumption that the sample is normally distributed and has a known standard deviation. The t-test is used to calculate the t-value, which is then compared with a critical value to determine whether the null hypothesis should be rejected.Example Problem
Suppose a researcher wants to know whether the average weight of a particular population of dogs is 20 pounds. The researcher takes a sample of 25 dogs from the population and measures their weight. The sample mean weight is 22.5 pounds, with a standard deviation of 3 pounds. The researcher wants to test whether the sample mean weight is significantly different from the hypothesized population mean of 20 pounds.To solve this problem, the researcher can use the one-sample t-test. The null hypothesis is that the sample mean weight is equal to 20 pounds, while the alternative hypothesis is that the sample mean weight is different from 20 pounds. The level of significance is set at 0.05.
Solution
The formula to calculate the t-value is:
t = (x̄ - μ) / (s / √n)
where x̄ is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
Substituting the values from the problem:
t = (22.5 - 20) / (3 / √25) = 5 / 0.6 = 8.33
The degrees of freedom (df) for one-sample t-test is n-1, which is 24 in our example.
Using a t-distribution table, we find that the critical value for a two-tailed test with df=24 and α=0.05 is ±2.064.
Since the calculated t-value (8.33) is greater than the critical value (2.064), we reject the null hypothesis and conclude that the sample mean weight is significantly different from the hypothesized population mean of 20 pounds.