09 Inference for Means and Proportions Free Online FlashCards

What is the 10% condition?

For sampling without replacement, the sample should be no more than about 10% of the finite population.

How are a two-sided test and matching confidence interval connected?

A two-sided confidence interval excludes the null value when the corresponding two-sided test rejects at the matching significance level.

Why should statistical significance not be treated as practical importance?

Statistical significance does not guarantee practical importance; interpret the estimated effect's size and context as well as its p-value.

Which proportion belongs in a one-proportion test's standard error?

For a one-proportion hypothesis test, use the null proportion in the standard error: $\sqrt{\frac{p_0(1-p_0)}{n}}$.

What standard error is used for a large-sample proportion interval?

A one-proportion confidence interval uses the sample proportion: $\hat p\pm z^*\sqrt{\frac{\hat p(1-\hat p)}{n}}$.

When is a one-sample $t$ interval used?

A one-sample $t$ interval uses $\bar x\pm t^*_{\alpha/2,n-1}\frac{s}{\sqrt n}$ when the population standard deviation is unknown.

What is the one-sample $t$ statistic?

For a one-mean test, $t=\frac{\bar x-\mu_0}{s/\sqrt n}$, with $n-1$ degrees of freedom.

Why is a two-proportion interval generally unpooled?

For two independent proportions, a confidence interval for $p_1-p_2$ generally uses separate, unpooled sample-proportion standard errors.

When is a pooled proportion used?

For testing $H_0:p_1-p_2=0$, combine the successes and sample sizes to estimate $\hat p_{\mathrm{pool}}=\frac{x_1+x_2}{n_1+n_2}$.

When should Welch's two-sample method be preferred?

Welch's method is the safer default when population variances are not known to be equal, especially when sample sizes or sample standard deviations differ substantially.

What assumption justifies a pooled two-sample procedure?

A pooled two-sample procedure assumes equal population variances: $\sigma_1^2=\sigma_2^2=\sigma^2$.

How are paired observations analyzed?

Paired data are reduced to within-pair differences, such as $d_i=\mathrm{after}_i-\mathrm{before}_i$, and analyzed as a one-sample mean problem.