When to use z or t statistics in significance tests | AP Statistics | Khan Academy | Summary and Q&A

TL;DR

This video explains when to use a z statistic versus a t statistic for significance tests in statistics.

Key Insights

• 🤪 Significance tests for proportions involve setting up a null hypothesis, calculating the sample proportion, and determining the probability using a z statistic.
• 🤐 When dealing with means, estimating the standard deviation of the underlying population allows for the calculation of the t statistic instead of the z statistic.
• 🔠 The t statistic provides a more accurate estimate of the probability in cases where the standard deviation is unknown.
• 🤐 The standard error of the statistic is crucial in the calculation of both the z statistic and the t statistic.
• ⚾ The P-value is used to assess the significance of the observed proportion or mean, based on the null hypothesis.
• 💼 In both cases, the alternative hypothesis determines whether the observed proportion or mean is greater than, less than, or not equal to the assumed value.
• 🏆 Proportions and means are two common scenarios in significance tests, each requiring a different statistical approach.

Transcript

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Questions & Answers

Q: When should a z statistic be used?

A z statistic should be used when conducting a significance test for proportions. It helps determine the probability of getting a sample proportion at least as extreme as the observed proportion, assuming the null hypothesis is true.

Q: How is the P-value calculated for proportions?

The P-value for proportions is calculated by finding the difference between the sample proportion and the assumed proportion from the null hypothesis, divided by the standard error of the sampling distribution of the sample proportion.

Q: Why is a t statistic used for means instead of a z statistic?

A t statistic is used for means because the standard deviation of the underlying population is often unknown. Instead, it is estimated using the sample standard deviation. The t statistic provides a better estimate of the probability in this case.

Q: How is the standard error of the mean estimated?

The standard error of the mean is estimated by dividing the sample standard deviation by the square root of the sample size. This is used in the calculation of the t statistic for means.

Summary & Key Takeaways

• When dealing with proportions, a significance test is conducted by setting up a null hypothesis about the population proportion and calculating the sample proportion and P-value.

• The P-value is calculated by finding the difference between the sample proportion and the assumed proportion from the null hypothesis, divided by the standard error of the sampling distribution of the sample proportion.

• When dealing with means, a null hypothesis is set up about the population mean, and the sample mean is calculated. To calculate the standard error of the mean, the standard deviation of the underlying population is needed, which is estimated using the sample standard deviation.