Large sample proportion hypothesis testing | Probability and Statistics | Khan Academy | Summary and Q&A

TL;DR

Testing whether more than 30% of U.S. households have internet access using hypothesis testing with a significance level of 5%.

Key Insights

• 🏆 The hypothesis test aims to determine whether the observed sample proportion is statistically significant evidence to reject the null hypothesis.
• ❓ The normal distribution is used as an approximation for the distribution of sample proportions when certain conditions are met.
• 🤪 The critical Z-value is used to determine the probability of obtaining a result as extreme or more extreme than the observed sample proportion.
• 🎚️ The probability of obtaining the observed sample proportion or a more extreme result is compared to the significance level (5%) to make a decision about rejecting or not rejecting the null hypothesis.
• 🤪 In this case, the observed sample proportion is more extreme than the critical Z-value, thus leading to the rejection of the null hypothesis in favor of the alternative hypothesis.
• 😀 This analysis demonstrates the process of hypothesis testing using a proportion and highlights the importance of understanding significance levels and interpreting P-values.

Transcript

We want to test the hypothesis that more than 30% of U.S. households have internet access with a significance level of 5%. We collect a sample of 150 households, and find that 57 have access. So to do our hypothesis test, let's just establish our null hypothesis and our alternative hypothesis. So our null hypothesis is that the hypothesis is not co... Read More

Questions & Answers

Q: What is the null hypothesis in this hypothesis test?

The null hypothesis states that the proportion of U.S. households with internet access is less than or equal to 30%.

Q: What is the alternative hypothesis in this hypothesis test?

The alternative hypothesis states that the proportion of U.S. households with internet access is greater than 30%.

Q: How is the sample proportion calculated?

The sample proportion is calculated by dividing the number of households with internet access in the sample by the total number of households in the sample.

Q: How is the standard deviation of the sample proportions distribution calculated?

The standard deviation is calculated by taking the square root of the product of the assumed proportion of households with internet access under the null hypothesis and the proportion of households without internet access, divided by the square root of the sample size.

Summary & Key Takeaways

• The null hypothesis is that the proportion of U.S. households with internet access is less than or equal to 30%.

• The alternative hypothesis is that the proportion is greater than 30%.

• The sample proportion is calculated to be 0.38, which is used to determine the probability of getting this result assuming the null hypothesis.