One Sample T-Test Example Problems With Solutions Pdf

Introduction

In the field of statistics, hypothesis testing is a commonly used method to determine the significance of observed differences between two or more groups. One-sample t-test is a type of hypothesis test used to compare the mean of a sample to a known or hypothesized population mean. This test is commonly used in research studies, clinical trials, and many other fields. In this article, we will provide a comprehensive guide about one sample t-test with example problems and solutions in pdf format that can help you understand the test better.

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

Related PDF

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.

Conclusion

One-sample t-test is a useful statistical tool for testing hypotheses about the mean of a population based on a sample mean. Through this article, we have provided an example problem and solution for one-sample t-test, along with a brief introduction about the test. These solutions are available in pdf format, which can be useful for students or researchers who are learning about this topic. By understanding the one-sample t-test, researchers can make more informed decisions about their research or clinical trials, leading to better outcomes.