# inferential statistics

Directions

Calculate a 95% confidence interval for each of your survey questions (1–6). Your final product should have six confidence intervals.
Perform a hypothesis test for each survey question (1–6). Your final product should have six hypothesis tests.

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When determining the two hypotheses for each question, how do you know what to compare the population parameter to? Honestly, we do not know, but we can make an educated guess. First, since we have sample proportions and means to consider, remember that the sample statistics always support the alternative hypothesis. Why? Hypothesis testing always tries to reject the null hypothesis; thus, we must have some evidence (the sample statistics) that the alternative is correct. Outside of this requirement, feel free to use any logical value in your hypothesis test.
A few notes, however:

We always think the alternative hypothesis is correct! This means the sample statistics (the sample proportion or mean) support the alternative hypothesis.
You probably want to write the alternative hypothesis first. Then, the null hypothesis is just the opposite of the alternative.
The two hypotheses must be the exact opposites of each other. We cannot put one value for the null and another for the alternative; that simply is not logical.
For questions 1–4, we are using the sample proportion to estimate the population proportion. For questions 5–6, we are using the sample mean to estimate the population mean. Thus, we use different formulas for their confidence intervals and for their test statistics in the hypothesis tests.

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