How to Calculate Test Statistics for Hypothesis Testing

TL;DR

To calculate test statistics for hypothesis testing, use the z or t formulas based on sample size and standard deviation. For a sample size under 30 with an unknown population standard deviation, use the t-distribution. For larger samples or known population standard deviations, use the normal distribution to determine whether to reject or not reject the null hypothesis.

Transcript

let's say that you're solving a problem associated with hypothesis testing and let's say that the null hypothesis is that the mean is 50 and that for the alternative hypothesis let's say someone believes that the mean is not 50 and decides to conduct a test how do you know if the null hypothesis should be rejected or not rejected for this example w... Read More

Key Insights

• ❓ Hypothesis testing involves comparing a null hypothesis with an alternative hypothesis.
• 🤐 Test statistics, such as z or t values, are calculated to determine whether the null hypothesis should be rejected.
• 🌥️ Test statistic formulas vary based on the scenario: population mean, population mean with known standard deviation, population mean with large sample size, and population proportion.
• 😃 The t-distribution is used when the sample size is less than 30 and the population standard deviation is unknown.
• 🤪 The normal distribution (z-value) is used when the sample size is larger than 30, regardless of the knowledge of the population standard deviation.
• 💁 Different formulas are used for calculating the test statistic depending on the scenario (mean or proportion) and available information (sample size and standard deviation).

Questions & Answers

Q: How do you know if the null hypothesis should be rejected or not in hypothesis testing?

To determine if the null hypothesis should be rejected, you need to calculate a test statistic (z or t value) and compare it to the critical value. If the calculated value falls within the rejection region (shaded area), the null hypothesis is rejected; otherwise, it is not.

Q: When should the t-distribution be used instead of the normal distribution in hypothesis testing?

The t-distribution should be used when the sample size is less than 30 and the population standard deviation is unknown. In this case, the test statistic is calculated using the t-value formula, which accounts for greater uncertainty with smaller sample sizes.

Q: What formula should be used to calculate the test statistic when both the sample size and population standard deviation are known (n > 30)?

When the sample size is larger than 30 and the population standard deviation is unknown, the test statistic is calculated using the z-value formula. The z is obtained by dividing the difference between the sample mean and population mean by the sample standard deviation over the square root of n.

Q: How is the test statistic calculated for hypothesis testing involving population proportions?

When dealing with population proportions, the test statistic is calculated using the z-value formula. It involves the difference between the sample proportion and population proportion divided by the square root of pq over n, where q is one minus the population proportion.

Summary & Key Takeaways

• Hypothesis testing involves comparing a null hypothesis (often the mean is a specific value) with an alternative hypothesis.

• To determine if the null hypothesis should be rejected or not, a calculated z (or t) value is compared to the critical value.

• Test statistics vary depending on the scenario: population mean (using z or t value), population mean with known standard deviation (using z value), population mean with large sample size (using z value), and population proportion (using z value).