# Hypothesis Test and Confidence Interval for Two Populations Means in StatCrunch | Summary and Q&A

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September 28, 2018
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The Math Sorcerer
Hypothesis Test and Confidence Interval for Two Populations Means in StatCrunch

## TL;DR

A hypothesis test is performed to determine if the weights of diet soda cans are less than regular soda cans.

## Key Insights

• ๐ The null hypothesis, mu1 = mu2, is written down for a hypothesis test comparing the weights of diet soda cans and regular soda cans.
• ๐คข T-statistics are used in the hypothesis test because only sample standard deviations are given, indicating the use of a t-distribution.
• ๐ฅบ The test statistic, T, is calculated as -8.5124, and the p-value is less than 0.01, leading to the rejection of the null hypothesis.
• ๐ The conclusion of the hypothesis test supports the claim that the mean weight of diet soda cans is less than the mean weight of regular soda cans.
• ๐งก A confidence interval is calculated, which further supports the conclusion of the hypothesis test by providing a range of values that only includes negative numbers.
• ๐ The content emphasizes the importance of being careful with the calculations and double-checking the numbers to ensure accuracy in hypothesis tests.
• ๐ The use of Statcrunch is demonstrated as a tool for performing the hypothesis test and calculating the confidence interval.

## Transcript

this problem we appear to have a hypothesis test and looks like there's two means we have mu 1 and mu 2 if we look at the last sentence it says test the claim that the contents of cans of diet soda have weights with the mean that is less than the mean for regular soda so this is a hypothesis test for two means so the first step in any hypothesis te... Read More

### Q: What is the first step in conducting a hypothesis test for two means?

The first step is to write down the null and alternative hypotheses, which in this case is mu1 = mu2.

### Q: When should Z-statistics be used instead of T-statistics in hypothesis tests for means?

Z-statistics are used when the population standard deviation is given. In this case, T-statistics are used because only the sample standard deviations are provided.

### Q: How is the test statistic calculated in the hypothesis test?

The test statistic is T, which is calculated using the sample means, sample standard deviations, and sample sizes of the two groups being compared.

### Q: What is the significance level commonly used in hypothesis tests?

The significance level, denoted as alpha, is typically set at 0.05.

## Summary & Key Takeaways

• The content discusses the process of conducting a hypothesis test for two means, specifically comparing the weights of diet soda cans to regular soda cans.

• The first step is to write down the null and alternative hypotheses, which in this case is mu1 = mu2, where mu1 represents the mean weight of diet soda cans and mu2 represents the mean weight of regular soda cans.

• The content explains the use of T-statistics instead of Z-statistics in this particular scenario and provides instructions on using Statcrunch to perform the hypothesis test.