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What is the formula for the test statistic (t-score) in a one-sample t-test?
$t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}$ where $\bar{x}$ is the sample mean, $\mu_0$ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.
What is the formula for the test statistic (z-score) in a one-sample proportion z-test?
$z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}}$ where $\hat{p}$ is the sample proportion, $p_0$ is the hypothesized population proportion, and n is the sample size.
Explain the concept of statistical significance.
Statistical significance indicates that the observed result is unlikely to have occurred by random chance alone, assuming the null hypothesis is true. A small p-value suggests statistical significance.
Explain the role of the significance level (alpha) in hypothesis testing.
The significance level (alpha) is the probability of rejecting the null hypothesis when it is actually true (Type I error). It sets the threshold for determining statistical significance; typically, alpha is set to 0.05.
Explain Type I error in hypothesis testing.
A Type I error occurs when the null hypothesis is rejected when it is actually true (false positive). The probability of making a Type I error is equal to the significance level (alpha).
Explain Type II error in hypothesis testing.
A Type II error occurs when the null hypothesis is not rejected when it is actually false (false negative).
What are the differences between a Type I error and a Type II error?
Type I error: Rejecting a true null hypothesis. | Type II error: Failing to reject a false null hypothesis.
What are the differences between a one-tailed test and a two-tailed test?
One-tailed test: Tests for a difference in one direction. | Two-tailed test: Tests for a difference in either direction.