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

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November 3, 2010
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Large sample proportion hypothesis testing | Probability and Statistics | Khan Academy

## TL;DR

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

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### 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.